The Mental Health Education Management of Higher Vocational Students Based on Fractional Differential Equations

Based on fractional differential equations, this paper proposes an optimization modeling method for the mental health quality of vocational students. This article quantifies the psychology of higher vocational students from the perspective of fractional differential equations. At the same time, we use alertness to characterize the risk of mental fatigue and propose a mental health energy equation. We propose a mental health energy replenishment function and consumption function and describe mental health energy during sleep. Finally, we use fractional differential equations to reason about the model deductively. The research shows that it is feasible for us to apply fractional differential equations to predict the mental health problems of vocational students.


Introduction
Their psychology largely influences the behavior of higher vocational students.The various forms of psychology determine the diversity of students' behavior in higher vocational colleges.The behavior of higher vocational students is not only affected by subjective factors such as their psychological cognition level but also by objective factors such as changes in society, school, and family environment [1].Therefore, improving the health quality of higher vocational students has become the main problem to be solved urgently in the current ideological and political education work in colleges and universities.This has also become the focus of research by relevant experts and scholars in ideological education.Some scholars have proposed an optimization modeling method of higher vocational students' mental health quality based on granularity transformation.Some scholars have proposed an optimization modeling method for the mental health quality of higher vocational students based on the introduction of characteristic tendencies.Based on kernel clustering, some scholars have proposed an optimization modeling method of higher vocational students' mental health quality [2].These traditional methods generally have the problems of low modeling accuracy, complicated modeling process, and long time-consuming.Therefore, we propose an optimal modeling method for higher vocational students' mental health quality based on fractional differential equations.

The principle model of higher vocational students' psychological information system
In establishing the principle model of the higher vocational students' psychological information system, we first obtain the outstanding psychological and physiological characteristics of the higher vocational students.Through this feature, we analyze the objective factors of the external environment and the main factors of the higher vocational students' psychological production [3].At the same time, the paper builds the principle model of the higher vocational students' psychological information system.The specific steps are detailed as follows: y represents the characteristic variables of the psychological and physiological outstanding performance of vocational students [4].The characteristic variable of the mental state of vocational students is 1 2 ( , , , ) . At the same time, the variable y is affected by the change of variable x or 1 2 ( , , , ) . However, the value of y is not unique when the main factor y or 1 2 ( , , , ) of vocational students is given.Therefore, we know that there is a correlation between the psychology of higher vocational students and their main factors.We use formula (1) to express the linear relationship between the two ( , ) ( , , , , ) There is a corresponding correlation between the psychological state characteristics of higher vocational students and the variable observations of their main factors [5].We use (3) to express ( , ) 1, 2, , ( , , , , , ) In the above relationship m represents the random error between variable relationships.We use formula (5) to represent the principal model of the higher vocational students' psychological information system.We use the principle model of higher vocational students' psychological information system to optimize the modeling of mental health quality.At this point, we should analyze the relationship between psychology and behavioral barriers in great detail.But the traditional method is to introduce a mapping table and a threshold for the misclassification rate [6].We need to complete the modeling according to the attributes of different mental health quality categories.However, this method is difficult to extract the characteristics of vocational students' psychological phenomena accurately.At the same time, this method has the problem of large modeling errors.Therefore, we propose an optimal modeling method for higher vocational students' mental health quality based on fractional differential equations.

The formation of the stage of rebellious psychological activities of higher vocational students
We obtained the essence of higher vocational students' psychology in modeling the effect of higher vocational students' rebellious psychology on behavioral hindrance [7].At the same time, we give different stages of rebellious psychology of higher vocational students.At this time, the corresponding information entropy of the behavioral hindrance generated by each stage of the rebellious psychology of higher vocational students is obtained.We calculated the threshold of the behavioral tendency of higher vocational students to produce rebellious psychology.The specific process is as follows: { ( ), 1, 2, , } X t t n   represents the psychological time series set of vocational students at different stages.Due to the obvious differences in the manifestations of the rebellious psychology of higher vocational students, we need to reconstruct the phase space of the psychological formation process.At this point we get the matrix ) In the formula m represents the complexity of the rebellious psychology of higher vocational students, and  represents the psychological duration.It satisfies the following relation: We consider the rows in the matrix as multiple influences of inverse psychological change.Its total number is K .We rank according to the degree of resistance.At the same time, we can obtain the index of the affected categories of each influencing factor in the initial state of reverse psychological performance [8].We then obtained the reverse psychological performance states for different influence categories.The total number of m dimensional higher vocational students' psychological complexity corresponding to different psychological performance state sequences is m .We assume that the probability of occurrence of k kinds of different mental performance state sequences is 1 2 , , , k P P P  , then, according to the form of Shannon entropy, the probability of reverse mental state sequence is sorted.We use formula (8) to define the permutation entropy 1 ( ) We integrate the state sequence given by Eq. ( 8).We use Equation ( 9) to express the emotional characteristics of behavior corresponding to the reverse psychological state at this stage 0 / ( ) 1 represents the time series set of emotional, behavioral characteristics of higher vocational students' reversal psychological state [9].Due to the complexity of the behavioral tendency of higher vocational students dominated by rebellious psychology, it is necessary to establish a relational expression with the duration  of rebellious psychology.
We choose the duration series ( ) to form a new duration phase point column ( ) y t .At the same time, we determined the psychological duration  by calculating the correlation between ( )  x t and ( ) y t .The time-series sets of behavioral tendencies dominated by the rebellious psychology of vocational students in two different stages are set as X and Y .We screen out the average amount of information hindered by subjective and objective factors based on the performance of higher vocational students' rebellious psychology in work, life, and study.We use equations (10) and (11) to calculate the thresholds of behavioral inclinations caused by different reasons to form rebellious psychology.
( ) i Px x represents the time series set X of behavioral tendencies dominated by the rebellious psychology of higher vocational students formed by subjective will.i x represents the extracted feature index set of subjective factors such as emotional fluctuation, weak will, psychological conflict, extreme ideology, etc., ( ) i Py y represents the formed behavioral tendency time dominated by the psychology of higher vocational students formed by objective events [10].y represents the characteristic set of objective factors such as individualism, chasing fame and fortune, exploiting power for personal gain, offering and accepting bribes, and parents' education of their children is more focused on academic education.

Modeling of the relationship between higher vocational students' rebellious psychology and behavioral hindrance
We obtained the set of subjective and objective factors of higher vocational students' formation of rebellious psychology in modeling the effect of higher vocational students' rebellious psychology on behavioral hindrance [11].At the same time, we give the objective function of the relationship between the rebellious psychology of higher vocational students and their behavioral obstacles.A problem model of the effect of rebellious psychology on the behavioral hindrance of higher vocational students is established.The set of all factors that set the behavior tendency dominated by the rebellious psychology of higher vocational students is expressed as follows The generation of behavior is the resistance behavior that occurs when the objective events do not match the subjective will, and the obvious emotions such as psychological irritability and dissatisfaction cannot be resolved.So we divide X into c class.Suppose the set X contains c category attributes.At this time, we use formula (13) to express k a represents the various character factors that lead to the behavior of vocational students.k x represents the various resistance factors in the behavior of higher vocational students.X represents the implicit, conscious characteristic of the resistance of higher vocational students.R represents the explicit attitude characteristics of higher vocational students' personalities.We use Equation (15) to obtain the objective function of the relationship between the rebellious psychology of higher vocational students and their behavioral obstacles represents the strength of the association between each resistance emotion factor k x and the behavioral tendency category i v .Based on the evaluation function m ik u of the relationship between the psychological and behavioral hindrance obtained by the above formula, we use formula (16) to solve the optimal global solution ( ) )

Optimization modeling of mental health quality of vocational students
We set up a model of higher vocational students' psychological hindrance to behavior.At the same time, the article is based on the problem model of higher vocational students' rebellious psychology on behavioral hindrance.We use ant theory to solve the problem model.At this time, we effectively set up an optimization model for the mental health quality of higher vocational students.The specific process is as follows: ij  represents the tendency strength of higher vocational students' psychological hindering behavior in the t period.
represents the pheromone that ant k searches for the behavioral hindrance effect of higher vocational students' psychology. (01)     represents the effect of rebellion on behavior.We use formula (17) to calculate the tendency strength of hindering behavior in the search for the next period k z represents the length of the path traversed by the k ant in this cycle, then we have Q is a constant.Suppose ij  represents the visibility of path ( , ) i j .Usually, we take 1/ ij d .
We assume that ij d represents the length of the path ( , ) i j , and the importance corresponding to the visibility of the path is ( 0)    .The relative importance of the path trajectories is ( 0)    .U represents the feasible point set.The transition probability of ant k in the t time domain is , ( ) ij k p t , then we use formula (19) to define , ( ) At this time, we use the formula (20) to calculate the optimization function of the model of the influence of the rebellious psychology of higher vocational students on the behavior min ( ) .We use equation ( 21) to calculate the transition probability of ants We use formula (22) to optimize the mental health quality of vocational students  represents the increase in the regional attraction strength of j ants in this cycle.j L represents the amount of change in ( ) f X in this cycle.We define it as ( ) ( ) f X r f X   .We optimize the function with the help of the constant movement of m ants.When 0 ij   is satisfied, ant i transfers from its nearest neighbor i to ant j neighbor according to probability ij p .When 0 ij   is satisfied, the ant i searches the nearest neighbors.The search radius is r .At this time, it is expressed as individual ants or transferred to the location of other ants.

Psychological Fractional Differential Equations under Alertness Energy
When a person is relaxed, alertness t A can be replenished.So we use / t dA dt to denote the rate of change of alertness t A over time.Then the vigilance replenishment rate when a person is relaxed can be expressed as: After a person wakes up, the alertness energy t A does not accumulate and replenish but only consumes it, so the expression of the alertness energy replenishment rate after a person wakes up is: Therefore, the vigilance replenishment rate equation can be written as: Where H is the human state parameter.According to the vigilance replenishment rate formula (8)   .According to formula (23), the expression of vigilance kinetic energy A can be written as: (29) Then the specific expression of vigilance kinetic energy A when awake is:

Simulation results and analysis
We prove the comprehensive validity of the optimization model of mental health quality of vocational students based on fractional differential equations.At this point we need to experiment.This article builds a modeling simulation platform for higher vocational students' mental health quality under the environment of Matlab.We use questionnaires to conduct statistics.At the same time, the survey results are divided into 5 sample sets and 5 test sets.We use the model of this paper and the model of literature and literature to carry out statistical experiments on the optimization of the mental health quality of vocational students.We compare the three models' statistical efficiency (%) (Figure 1).

Figure 1
Comparison of statistical efficiency of different models The statistical efficiency of using the model in this paper to optimize the mental health quality of higher vocational students is higher than that of the literature and literature models.We use the model of this paper and the model of literature and literature to conduct statistical experiments on the effect of higher vocational students' psychology on behavioral hindrance.The statistical stability (%) of the effect of college psychology on behavioral hindrance was compared among the three models (Figure 2).

Figure 2 Comparison of statistical stability of different models
We use the model in this paper to calculate the statistical stability of higher vocational students' psychological hindrance to behavior, which is better than the literature and literature models.We use the model of this paper, and the model of literature and literature carry out statistical experiments on the optimization of the mental health quality of vocational students.We compare the three models to compare the statistical time complexity (%) of higher vocational students' mental health quality optimization modeling (Figure 3).

Figure 3 Comparison of statistical time complexity of different models
We use the model in this paper to optimize the mental health quality of higher vocational students.The statistical time complexity is lower than the literature and literature models.

Conclusion
This paper proposes an optimal modeling method for mental health higher vocational students based on fractional differential equations.The simulation results show that the proposed model has great advantages in modeling efficiency, stability, and time complexity.This provides a strong basis for improving the mental health of vocational students.T h i s p a g e i s i n t e n t i o n a l l y l e f t b l a n k a and b represent the correlation coefficient.The slope and intercept of the y a bx   relation are determined by a and b .

2
20) If the m ant is at an equal division of the interval m in the initial time domain, we replace ij  in Eq. (19) with j  .At this time, we call it the neighborhood attraction strength of ant j .We define ij  as the difference value of the objective function of the boring question model in the i j f f  interval of higher vocational students' rebellious psychological effect on behavioral hindrance.The parameter is denoted as , [1.5]    , a differential equation for the mental fatigue vigilance model can be obtained.