Information technology application ability is a necessary professional ability for teachers in the information society. The means to take effective measures to promote the acquisition and transfer of teacher information technology application ability involves undertaking measures to facilitate teachers to transform teaching methods, deepen basic education curriculum reform and promote teachers’ lifelong learning. It plays a vital role in effectively promoting the independent development of majors and further cracking the bottleneck problem of educational information development. This study uses the fractional differential equation method to select 220 elementary and middle school teachers in the Northeast Teacher Education Innovation Experimental Zone as the research objects. The research objects are measured by a scale and fractional differential equations are used to build a system that includes school factors, human factors, policy and institutional factors, training factors, self-efficacy factors and motivation factors of teacher information technology application ability transfer fractional differential equation influencing factor model; we hope to solve the problem of ‘learning and use disconnect’ in the process of teacher information technology application ability training, and to promote the effective transfer of teacher information technology application ability that can be used as an important reference.

#### Keywords

- fractional differential equation
- information technology application ability
- teacher education technology
- ability transfer

#### MSC 2010

- 97B10

The ‘National Medium and Long-term Educational Reform and Development Plan Outline (2010–2020)’ clearly states: ‘Information technology has a revolutionary impact on education development and must be highly valued’ (Ministry of Education, 2010). The construction of a contingent of teachers is the basic guarantee for the sustainable development of education informatisation, and the ability to apply information technology is a necessary professional ability for teachers in an information society. In October 2013, the Ministry of Education decided to implement the ‘National Primary and Secondary School Teachers’ Information Technology Application Ability Improvement Project’, which aims to systematically improve teacher information through the implementation of the three major links of ‘training-evaluation-application’ under the guidance of standard technical application capabilities. The above research points out the direction of related research on teacher information technology application ability training, that is, through the collection, processing and analysis of teacher information technology application ability transfer related data, exploration of factors that affect teacher information technology application ability transfer and formulation of the ability to promote ability transfer specific strategies. However, the existing research in this field still has shortcomings in the number of data samples and data analysis methods, and it is urgently necessary for future research to improve. This research will try to overcome the shortcomings of previous studies in sample size and data analysis methods, explore the factors affecting the transfer of teacher information technology application ability and build a model of related factors of fractional differential equations [1].

Through combing the relevant research at home and abroad, we conclude that the current factors affecting the transfer of teachers’ information technology application ability mainly include policy systems, schools, human activities, training, motivation and self-efficacy factors. Figure 1 shows a schematic diagram of the conditional assumption model. Therefore, this study makes the following assumptions:

H1: The software and hardware conditions of the teacher's school and the guarantee of time resources will affect the self-efficacy of teachers’ information technology application ability transfer.

H2: The software and hardware conditions, time arrangement and the strength of teachers in the training of teachers’ information technology application ability will affect the self-efficacy of teachers’ information technology application ability transfer.

H3: National or local related policies and systems will have an impact on the motivation of teachers’ information technology application ability transfer.

H4: School leaders, colleagues, students and domain experts have an impact on teachers’ motivation for the transfer of information technology application ability.

H5: National or local related policies and systems will have an impact on the school's human and material investment in teachers’ learning and use of information technology.

H6: National or local related policies and systems will have an impact on the quality of teachers’ participation in information technology application ability training.

H7: National or local policies and systems will affect the concepts, attitudes and practices of school leaders, colleagues, students and field experts on learning and applying information technology.

The model based on the above research assumptions is shown in Figure 1. The model contains six latent variables of school, training, policy system, human, self-efficacy and motivation. This study adopts the structural equation model method, through four steps of hypothetical model construction, model fitting, model evaluation and model modification, and finally builds a model of the influencing factors of the fractional differential equation of teacher information technology application ability transfer.

So far, there has been no unified definition expression for fractional calculus. Mathematicians analyse the problem from different angles and get different definitions. At this stage, there are three main definitions of fractional calculus: Grunwald-Let Niko definition (G-L), Riemann-Liouville definition (RL) and Capote definition. The definition of G-L is derived from the difference definition of integer-order differential. The definitions of RL and Capote are derived from the Cauchy formula of integral order. Using Gamma function Γ(

According to the derivation in the literature, when

The introduction of fractional integration theory into image denoising is a new development direction. If the duration of the unary signal

R-L defines the approximate expression of the

We perform partial fractional integration along eight directions (0°, 45°, 90°, 135°, 180°, 225°, 270° and 315°) of the pixels of the two-dimensional digital image, respectively, to construct eight 3

It is known that for any square integrable energy signal ^{2} (^{v}^{−v}= ^{v}

According to the theory of fractional operators, fractional differentiation and fractional integral are the inverse operations of each other, ^{−}= ^{′}

From Eqs (5) and (6), we draw the frequency response diagram of each order fractional derivative and integral.

A total of 206 valid questionnaires were collected in the research, including 25 male teachers and 181 female teachers, 16 teachers with postgraduate education, 183 undergraduates and 7 junior college graduates (Table 1). Analysing the test data of the scale using SPSS statistical analysis software, it can be concluded that the Cronbach's alpha of the scale is 0.912, which indicates that the test scale has good reliability and can be used for the next step of structural equation modelling construction.

Descriptive statistics of survey subjects

1 | Applying information technology to daily teaching will make my teaching behaviour more effective |

2 | Applying information technology to daily teaching will give me better career development opportunities |

3 | I am confident that in the course of teaching preparation, I can select appropriate information technology assistance (such as using PPT, Flash and web technologies to produce demonstration courseware) based on the course standard for the teaching design of the course |

4 | I am confident that in the classroom teaching process, I choose appropriate information technology (such as using simulation software to demonstrate the chemical reaction process) to promote student learning and improve classroom teaching effects |

5 | The state lists teachers’ information technology ability as an important indicator of teacher ability assessment, which will encourage me to apply information technology in daily teaching |

6 | If my province or city proposes a clear policy or action plan related to teacher information technology capabilities, it will encourage me to apply information technology in daily teaching |

7 | If the teacher's information technology application ability training can provide a good course structure and a software and hardware learning environment, it will help me apply information technology to daily teaching |

8 | If the teacher's information technology application ability training is reasonable in terms of class schedule and teacher staff, it will help me to apply information technology to daily teaching |

9 | If the teacher's information technology application ability training can provide high-quality training follow-up support (such as setting up discussion groups, answering support etc.), it will help me apply information technology to daily teaching |

10 | If the school can provide sufficient hardware guarantee for teachers to apply information technology (such as computers, high-speed broadband, multimedia classrooms, printers, scanners etc.), it will prompt me to apply information technology in daily teaching |

11 | If the school can provide sufficient software guarantee for teachers to apply information technology (such as office software, courseware production software, production material resources etc.), it will prompt me to apply information technology in daily teaching |

12 | If the school can give teachers a certain degree of teaching autonomy, it will help me apply information technology to daily teaching |

13 | If school leaders attach importance to teachers’ information technology application ability, it will prompt me to apply information technology in daily teaching |

14 | If my colleagues are keen to apply information technology to daily teaching, it will prompt me to apply information technology in daily teaching |

15 | If the students like it that the teacher applies information technology to daily teaching, it will help me to apply information technology to daily teaching |

16 | If domain experts are positive about applying information technology to daily teaching, it will prompt me to apply information technology in daily teaching |

Next, this research uses AMOS software to test the hypothesis model, including three steps: recognition calculation, fit detection and model correction:

Only on the premise that the model can be identified can we successfully estimate the various parameters in the model and complete the model's fit detection. This study adopts the t-law and uses the degrees of freedom to judge the degree of model recognition. Through calculation, the degree of freedom of the hypothetical model is ascertained to be 96, that is, the recognition degree of the model is over-recognition, which means that the next step of model fit detection can be performed [2].

This is mainly done by comparing the covariance matrix of the hypothetical model with the covariance matrix of the sample data. The closer the covariance matrix of the two is, the better the fit of the hypothetical model. It is difficult to judge whether the two covariance matrices are close to each other by simply observing the two covariance matrices. Therefore, the fit of the structural equation model is generally tested by the chi-square degree of freedom ratio (^{2}/^{2}) and the degree of freedom (

The smaller the chi-square degree of freedom ratio, the better the model fit. Generally speaking, the ratio of chi-square degrees of freedom <3 is acceptable; RMR is the mean square and square root of the residuals, which is the average value of the fitting residuals. Generally speaking, the smaller the RMR value, the better the model fit. The reference value of RMR is 0.05, and the value of RMR is >0.05, indicating that the hypothetical model needs to be revised; GFI is the fitness index, which measures the extent to which the covariance matrix of the sample data is predicted by the covariance matrix of the hypothetical model.

The reference value of GFI is 0.9 and the value of GFI is <0.9, indicating that the hypothetical model needs to be revised; RMSEA is the asymptotic residual mean square and square root. It is generally believed that the model with an RMSEA value >0.05 has a good fit; NFI is the standard fit index. It is generally believed that the model with an NFI value >0.9 has a good fit; CFI is a comparative fit index. It is generally believed that a model with a CFI value >0.9 has a good fit. The results of the analysis using AMOS software (Table 2) show that, except for the two index coefficients of the NFI and the CFI, the other index coefficients are not up to the standard, indicating that the fit of the hypothetical model is not good. We thus revise the hypothetical model.

Test index coefficients of model fit

Gender | Male | 25 | 12.1 |

Female | 181 | 87.9 | |

Education | Specialist | 7 | 3.4 |

Undergraduate | 183 | 88.8 | |

Postgraduate | 16 | 7.8 | |

Teaching age | 3 years and below | 5 | 2.5 |

3–10 years | 32 | 15.5 | |

10 (including 10 years) – 15 years | 40 | 19.4 | |

15 years and above | 129 | 62.6 | |

School nature | Municipal key primary and secondary schools | 51 | 24.8 |

Municipal primary and secondary schools | 113 | 54.9 | |

Primary and secondary schools below the county level | 42 | 20.3 |

After the model fit is tested, several correction suggestions are included in the analysis result report. The correction indicators include three sub-options of covariance, variance and regression coefficient. Generally speaking, model revision only adopts revision suggestions with revision index >5. After the analysis of the data, the suggestion to modify the model with a revised index >5 includes adding the communal relationship between e2 and e3 error variables, that is, adding the path from motivation to self-efficacy. The revised model path is shown in Figure 2 [3]. The test results of model fit after correction are shown in Table 3. It can be seen that, except for the residual mean square and square root index coefficient values being slightly higher than the standard value, the other index coefficients have reached the standard, indicating that the hypothetical model has a good fit. Compared with the hypothetical model, the revised model not only retains the original seven hypothetical influence paths but also adds an influence path from motivation to self-efficacy, that is, the motivation of teacher information technology application ability transfer will affect teachers’ information technology application ability, and the self-efficacy of migration has an impact. Based on the above analysis results, this research constructs a model of the influencing factors of teachers’ information technology application ability transfer fractional differential equations that includes school, human factors, policy systems, training, self-efficacy and motivation. Among them, self-efficacy and motivation are internal factors, whereas policy systems and training are external factors (Figure 3).

Modified model fitness test index coefficients

Reference | <3.00 | <0.05 | >0.90 | <0.05 | >0.90 | >0.90 |

Actual value | 3.311 | 0.092 | 0.857 | 0.078 | 0.974 | 0.973 |

CFI, comparative fit index; GFI, fitness index; NFI, standard fit index

Motivational factors refer to internal psychological factors related to teachers’ application of information technology to daily teaching. They stimulate, maintain and guide the transfer of teachers’ information technology application ability. Motivation is divided into intrinsic motivation and extrinsic motivation. It expresses the teacher's self-determination in the process of applying information technology, but the degree is different. Extrinsic motivation is accompanied by external pressure and experience requested by the outside world, and intrinsic motivation is accompanied by full personal will and choice. Generally speaking, teachers apply information technology to daily teaching as a necessary and sufficient condition to be qualified for the teaching profession; or teachers believe that certain teaching achievements can be brought about by applying information technology to daily teaching, for example, through the application of information technology in curriculum teaching activities, which can make classroom teaching achieve twice the result with half the effort; these are likely to form the internal motivation of teachers to apply information technology to daily teaching. Extrinsic motivation is the result of teachers being pressured by the outside world. In the model of the influencing factors of the fractional differential equation for the transfer of teachers’ information technology application ability, it is mainly manifested in the application of information technology to daily teaching, which is forced to be formed by the influence of policies, institutions and human activities.

Self-efficacy factors refer to teachers’ self-judgement and beliefs about applying information technology to daily teaching ability. Self-efficacy can be divided into result expectation and efficacy expectation. Efficacy expectation refers to the teacher's belief that he has the ability to successfully perform this specific behaviour; result expectation refers to the teacher's subjective judgement that a certain behaviour on one's part may lead to a certain result. Good results will activate the behaviour. The self-efficacy in this study specifically refers to the expectation of effectiveness, that is, teachers’ belief in applying the information technology they have learned to daily teaching. For example, teachers need to have the confidence to effectively apply the information technology they have mastered to daily teaching activities. Self-efficacy will also be affected by schools, training and motivation. If schools can provide teachers with sufficient software and hardware support, expert support and resource guarantees for teachers’ learning and application of information technology, it will be possible to improve teachers’ self-efficacy in applying information technology. The information technology training teachers participate in can be configured effectively in terms of teaching faculty, curriculum settings, practical support and knowledge transfer support, and it will be possible to improve teachers’ self-efficacy in applying information technology. In addition, experimental research data shows that the motivation of teachers’ information technology application ability transfer will also have a certain impact on self-efficacy [4].

This refers to the impact of non-human factors within the school on the application of information technology to teachers in daily teaching, including the school's school-running philosophy and operating mechanism, and whether the school has the ability to encourage teachers to learn advanced technology and apply it to specific subject teaching. Ideas and mechanisms will likely have an impact on teachers’ application of information technology to daily teaching; sufficient and high-quality hardware and software configurations will likely affect teachers’ application of information technology. In addition, the issue of whether the school can grant teachers a certain degree of teaching autonomy will also have a certain impact on teachers’ application of information technology. In addition to directly affecting the transfer of teachers’ information technology application ability, schools also indirectly affect teachers’ self-efficacy in applying information technology.

Training factors refer to the information technology training that teachers participate in, including training time arrangement, teacher allocation, curriculum setting, learning support and knowledge transfer support. High-quality information technology training may have a direct impact on teachers’ application of information technology to daily teaching. For example, if the training schedule, teacher allocation and curriculum settings can be arranged in a targeted manner with full consideration of the knowledge status and learning characteristics of the trained teachers, it will be possible to promote the teachers to obtain a solid information technology application ability and then apply information technology to daily teaching. If relevant training focuses not only on pre-training and training but also on knowledge transfer support after training, it may be beneficial to teachers to maintain and transfer the knowledge learned in training, and promote teachers to apply information technology in daily teaching activities. In addition, in addition to the direct impact on the transfer of teachers’ information technology application ability, training may also have an indirect impact by affecting self-efficacy.

This refers to national and local policies, systems and action plans related to teachers’ information technology application capabilities. The policy system is a relatively special factor in the fractional differential equation influencing factor model of the transfer of teachers’ information technology application ability. It does not directly affect the transfer of teachers’ information technology application ability, but does so indirectly through schools, training, and human and motivational factors that have an impact on teachers’ learning and application of information technology. It is the factor that has the most relational paths in the entire model. Generally speaking, national or local policies and systems related to teachers’ learning and application of information technology will directly affect schools’ support for the application of information technology in daily teaching, and also affect the attitudes and views of school leaders and colleagues towards information technology. Further, the motivation of teachers to learn and apply information technology in their teaching methods is affected; there is also an indirect impact on the transfer of teachers’ information technology application ability [5].

Human factors refer to factors from school leaders, colleagues, field experts and students that may have an impact on teachers’ learning and application of information technology. Human factors also do not directly affect the transfer of teachers’ information technology application ability, but indirectly play a role through motivation. Generally speaking, human factors are constituted by the views, attitudes and practices of school leaders on information technology, such as school leaders encouraging teachers to apply information technology in daily teaching activities; school leaders valuing teachers with higher levels of proficiency in information technology; colleagues’ views and attitudes towards information technology and practices, such as whether colleagues are keen on learning and applying information technology; teachers with higher levels of information technology being rewarded with a more prestigious position among colleagues; domain experts mainly referring to the views and attitudes of teaching method experts on information technology; and prevalence of the attitude of using advanced technology to assist teaching in daily teaching activities. All of the above may directly affect teachers’ motivation to apply information technology in daily teaching, and indirectly affect the transfer of teachers’ information technology application ability.

The construction of the model is not the ultimate goal of this research. This research hopes to clarify the factors that may affect the transfer of teachers’ information technology application ability and their mutual influences, so as to formulate teachers’ information technology application ability standards and select training models. We provide references for the construction of training resources and discuss a related evaluation system. Specific suggestions are as follows:

The role of national and local education management agencies in the transfer of teachers’ information technology application ability is mainly manifested in the formulation of corresponding policies, systems and incentive mechanisms to guide and encourage teachers to learn and master information technology, and effectively apply it to daily teaching. In the future process of teacher information technology application ability training, national and local education institutions should strengthen the formulation of relevant policies, systems and incentive mechanisms, simultaneously do a good job in publicity and promotion, and improve effective operating mechanisms so that teachers’ information technology application ability training is relevant. The work is carried out continuously, stably and normally. In addition, the relevant national functional departments should carry out innovations and improvements in the teacher qualification certificate system, take information technology application ability as one of the necessary standards for teacher professional access, and encourage and promote pre-service teachers to apply the information technology application ability acquired in the normal education stage to daily teaching [6].

The role of teacher education institutions in the transfer of teacher information technology application ability is mainly manifested in the following measures: organising teachers to participate in the corresponding information technology application ability courses, helping teachers to master basic information technology skills and applying the acquired information technology to them. Ensuring that teachers acquire the ability to effectively transfer information technology skills to the real classroom teaching environment necessitates exposing them to a framework of ongoing guidance and assistance. In the future, teachers’ information technology application ability training should refer to advanced foreign teacher education institution construction standards and accreditation systems, formulate a teacher education institution construction standard system and accreditation system that meets China's actual conditions and strengthen teacher education institutions’ institutional mechanisms, software and hardware infrastructure construction. The information technology application ability training curriculum system of teacher education institutions also needs to be continuously improved to increase the proportion of practical courses. In addition, teacher education institutions should not be limited to ‘one-time training’, but should be based on the construction of a lifelong learning system for teachers’ information technology application ability training, which ideally needs to be designed in such a way as to promote the effective transfer of teachers’ information technology application ability [7, 8].

The role of schools in the transfer of teachers’ information technology application ability is mainly manifested in environmental construction, including soft and hard environments [9,10]. The soft environment mainly refers to the school's school-running philosophy, measures to promote the professional development of teachers and the application of information technology atmosphere created by school leaders and colleagues; the hard environment mainly refers to the school's software and hardware infrastructure construction, learning resource construction etc. In the future process of cultivating teachers’ information technology application ability, schools should not only increase their efforts in the construction of the hard environment but also pay attention to the construction of the soft environment, encourage teachers to learn information technology, give teachers a certain degree of teaching autonomy and motivate teachers to effectively capitalise on their information technology skills in the day-to-day teaching environment; and doing so will go a long way in ensuring that teachers effectively apply the learned information technology skills in teaching activities, improve teaching efficiency, form a good learning atmosphere of ‘leadership support, teachers’ enthusiasm’ in the school and promote the effective transfer of teachers’ information technology application ability.

To summarise, based on the structural equation model, this study constructed a model of the influencing factors of teacher information technology application ability transfer fractional differential equations containing six influencing factors of fractional differential equations. The mutual influence relationship is clearly defined.

#### Descriptive statistics of survey subjects

1 | Applying information technology to daily teaching will make my teaching behaviour more effective |

2 | Applying information technology to daily teaching will give me better career development opportunities |

3 | I am confident that in the course of teaching preparation, I can select appropriate information technology assistance (such as using PPT, Flash and web technologies to produce demonstration courseware) based on the course standard for the teaching design of the course |

4 | I am confident that in the classroom teaching process, I choose appropriate information technology (such as using simulation software to demonstrate the chemical reaction process) to promote student learning and improve classroom teaching effects |

5 | The state lists teachers’ information technology ability as an important indicator of teacher ability assessment, which will encourage me to apply information technology in daily teaching |

6 | If my province or city proposes a clear policy or action plan related to teacher information technology capabilities, it will encourage me to apply information technology in daily teaching |

7 | If the teacher's information technology application ability training can provide a good course structure and a software and hardware learning environment, it will help me apply information technology to daily teaching |

8 | If the teacher's information technology application ability training is reasonable in terms of class schedule and teacher staff, it will help me to apply information technology to daily teaching |

9 | If the teacher's information technology application ability training can provide high-quality training follow-up support (such as setting up discussion groups, answering support etc.), it will help me apply information technology to daily teaching |

10 | If the school can provide sufficient hardware guarantee for teachers to apply information technology (such as computers, high-speed broadband, multimedia classrooms, printers, scanners etc.), it will prompt me to apply information technology in daily teaching |

11 | If the school can provide sufficient software guarantee for teachers to apply information technology (such as office software, courseware production software, production material resources etc.), it will prompt me to apply information technology in daily teaching |

12 | If the school can give teachers a certain degree of teaching autonomy, it will help me apply information technology to daily teaching |

13 | If school leaders attach importance to teachers’ information technology application ability, it will prompt me to apply information technology in daily teaching |

14 | If my colleagues are keen to apply information technology to daily teaching, it will prompt me to apply information technology in daily teaching |

15 | If the students like it that the teacher applies information technology to daily teaching, it will help me to apply information technology to daily teaching |

16 | If domain experts are positive about applying information technology to daily teaching, it will prompt me to apply information technology in daily teaching |

#### Modified model fitness test index coefficients

Reference | <3.00 | <0.05 | >0.90 | <0.05 | >0.90 | >0.90 |

Actual value | 3.311 | 0.092 | 0.857 | 0.078 | 0.974 | 0.973 |

#### Test index coefficients of model fit

Gender | Male | 25 | 12.1 |

Female | 181 | 87.9 | |

Education | Specialist | 7 | 3.4 |

Undergraduate | 183 | 88.8 | |

Postgraduate | 16 | 7.8 | |

Teaching age | 3 years and below | 5 | 2.5 |

3–10 years | 32 | 15.5 | |

10 (including 10 years) – 15 years | 40 | 19.4 | |

15 years and above | 129 | 62.6 | |

School nature | Municipal key primary and secondary schools | 51 | 24.8 |

Municipal primary and secondary schools | 113 | 54.9 | |

Primary and secondary schools below the county level | 42 | 20.3 |

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Management Model of Large Companies Based on Mathematical Statistics Equations Data Forecasting of Air-Conditioning Load in Large Shopping Malls Based on Multiple Nonlinear Regression System dynamics model of output of ball mill Optimisation of Modelling of Finite Element Differential Equations with Modern Art Design Theory Mathematical function data model analysis and synthesis system based on short-term human movement Sensitivity Analysis of the Waterproof Performance of Elastic Rubber Gasket in Shield Tunnel Human gait modelling and tracking based on motion functionalisation Analysis and synthesis of function data of human movement The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Financial Accounting Measurement Model Based on Numerical Analysis of Rigid Normal Differential Equation and Rigid Functional Equation Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Design of Morlet wavelet neural network to solve the non-linear influenza disease system Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate Differential equation model of financial market stability based on Internet big data 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System Children’s cognitive function and mental health based on finite element nonlinear mathematical model Motion about equilibrium points in the Jupiter-Europa system with oblateness Fractional Differential Equations in Electronic Information Models Badminton players’ trajectory under numerical calculation method BIM Engineering Management Oriented to Curve Equation Model Optimal preview repetitive control for impulse-free continuous-time descriptor systems Development of main functional modules for MVB and its application in rail transit Study on the impact of forest fire prevention policy on the health of forest resources Mathematical Method to Construct the Linear Programming of Football Training The Size of Children's Strollers of Different Ages Based on Ergonomic Mathematics Design Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method Value Creation of Real Estate Company Spin-off Property Service Company Listing Selection by differential mortality rates Digital model creation and image meticulous processing based on variational partial differential equation Dichotomy model based on the finite element differential equation in the educational informatisation teaching reform model Nonlinear Dissipative System Mathematical Equations in the Multi-regression Model of Information-based Teaching The modelling and implementation of the virtual 3D animation scene based on the geometric centre-of-mass algorithm The policy efficiency evaluation of the Beijing–Tianjin–Hebei regional government guidance fund based on the entropy method The transfer of stylised artistic images in eye movement experiments based on fuzzy differential equations Research on behavioural differences in the processing of tenant listing information: An eye-movement experiment A review of the treatment techniques of VOC Some classes of complete permutation polynomials in the form of ( x ^{pm}−x +δ )^{s}+ax ^{pm}+bx overF _{p2m}The consistency method of linguistic information and other four preference information in group decision-making Research on the willingness of Forest Land’s Management Rights transfer under the Beijing Forestry Development A mathematical model of the fractional differential method for structural design dynamics simulation of lower limb force movement step structure based on Sanda movement Fractal structure of magnetic island in tokamak plasma Numerical calculation and study of differential equations of muscle movement velocity based on martial articulation body ligament tension Study on the maximum value of flight distance based on the fractional differential equation for calculating the best path of shot put Sports intensity and energy consumption based on fractional linear regression equation Analysis of the properties of matrix rank and the relationship between matrix rank and matrix operations Study on Establishment and Improvement Strategy of Aviation Equipment Research on Financial Risk Early Warning of Listed Companies Based on Stochastic Effect Mode Characteristics of Mathematical Statistics Model of Student Emotion in College Physical Education Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Nonlinear strategic human resource management based on organisational mathematical model Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Fractional Differential Equations in Sports Training in Universities Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model