Zeitschriftendaten
Format
Zeitschrift
eISSN
2444-8656
Erstveröffentlichung
01 Jan 2016
Erscheinungsweise
2 Hefte pro Jahr
Sprachen
Englisch
Uneingeschränkter Zugang

# Fractional Differential Equations in the Standard Construction Model of the Educational Application of the Internet of Things

###### Akzeptiert: 31 Mar 2022
Zeitschriftendaten
Format
Zeitschrift
eISSN
2444-8656
Erstveröffentlichung
01 Jan 2016
Erscheinungsweise
2 Hefte pro Jahr
Sprachen
Englisch
Introduction

The Internet of Things connects all objects through perception technology and identification technology and the Internet for information exchange and communication [1]. This provides universal data analysis and services based on heterogeneous Internet infrastructure and ubiquitous sensors and networks. It finally realizes the one-to-one mapping relationship between data and objects and provides query interfaces [2]. This paper proposes a discrete system differential data fusion guided by integral discrete in the Internet of Things. We first adopt the Internet of Things technology to uniformly collect and integrate the terminal data of each discrete manufacturing system under the distributed system. In addition, after summarizing all the information, we use the integral discrete guidance method to process all the differentiated data obtained to achieve the effective fusion of all data [3]. Finally, we use a set of 6 types of data of 100 nodes to test the system's performance.

Proposal of Integral Discrete Guided Algorithm

An integral discrete guidance algorithm is an algorithm that uses the calculus method to fuse and uniformly process the distributed and differentiated data in the system network. We use the integration idea under the distributed system to organically combine various data in the network system [4]. Finally, the efficient integration of differentiated data is realized. The system model of the integral discrete guidance algorithm is defined as: ${E(I)=∫Ω|DυI‖dxdy+2¯‖I0−I‖L22I∈BVυ(Ω)x∈Ωy∈Ω$ \left\{{\matrix{{E\left(I \right) = \int_\Omega {\left| {{D^\upsilon}I\left\| {dxdy + \bar 2\left\| {{I_0} - I} \right\|_{{L_2}}^2} \right.} \right.}} \hfill \cr {I \in B{V^\upsilon}\left(\Omega \right)} \hfill \cr {x \in \Omega} \hfill \cr {y \in \Omega} \hfill \cr}} \right.

$|DυI|=(DxυI)2+(DyυI)2$ \left| {{D^\upsilon}I} \right| = \sqrt {{{\left({D_x^\upsilon I} \right)}^2} + {{\left({D_y^\upsilon I} \right)}^2}} is the system model of the integral discrete guided algorithm. $DxυI$ D_x^\upsilon I is the integral derivative of the integral discrete guidance algorithm concerning point x. $DyυI$ D_y^\upsilon I is the integral derivative of the integral discrete guidance algorithm concerning point y.

We need to adopt the minimization thought processing method in the integral discrete guidance algorithm [5]. Therefore, we use the variational nature of the integral discrete guided algorithm to construct the corresponding differential data guiding function, which we define as: $g(ε)=E(I+εφ)=∫Ω|Dυ(I+εφ)I||dxdy+λ2||I0−I−εφ||L22$ g\left(\varepsilon \right) = E\left({I + \varepsilon \varphi} \right) = \int_\Omega {\left| {{D^\upsilon}\left({I + \varepsilon \varphi} \right)I} \right|\left| {dxdy + {\lambda \over 2}} \right|\left| {{I_0} - I - \varepsilon \varphi} \right||_{{L_2}}^2}

ε is any real number. φ is an arbitrary function. We use different data to guide the basic properties of functional extremes [6]. When $φ∈C0∞(Ω)$ \varphi \in C_0^\infty \left(\Omega \right) and $gε'(0)=0$ g_\varepsilon^{'}\left(0 \right) = 0 , the corresponding solution guiding equation can be obtained: $∫Ω(DxυI|DυI|Dxυφ+DyυI|DυI|Dyυφ)dxdy−λ∫Ω(I0−I)φL2dxdy$ \int_\Omega {({{D_x^\upsilon I} \over {\left| {{D^\upsilon}I} \right|}}D_x^\upsilon \varphi + {{D_y^\upsilon I} \over {\left| {{D^\upsilon}I} \right|}}D_y^\upsilon \varphi)dxdy - \lambda \int_\Omega {({I_0} - I){\varphi _{{L_2}}}dxdy}}

We need to eliminate arbitrary functions to get the final difference data guide model. Therefore, ϕ adopts the identity formula in the differential data guidance model of discrete integral guidance: $∫Ωfgdxdy=λ2π∫Ωf^ g^¯dω1dω2=0$ \int_\Omega {fgdxdy = {\lambda \over {2\pi}}\int_\Omega {\hat f\,{\bar {\hat g}}d{\omega _1}d{\omega _2} = 0}}

Processing the difference data fusion algorithm guided by integral discrete can get: $λ2π∫Ω(D^xυφD^xυI¯|DυI|+D^yυφD^yυI¯|DυI|)dω1dω2−λ22π∫Ωφ^(I^0¯−I^¯)dω1dω2=0$ {\lambda \over {2\pi}}\int_\Omega {({\hat D}_x^\upsilon \varphi {{\overline {{\hat D}_x^\upsilon I}} \over {\left| {{D^\upsilon}I} \right|}} + {\hat D}_y^\upsilon \varphi {{\overline {{\hat D}_y^\upsilon I}} \over {\left| {{D^\upsilon}I} \right|}})} d{\omega _1}d{\omega _2} - {{{\lambda ^2}} \over {2\pi}}\int_\Omega {{\hat \varphi} (\overline {{{\hat I}_0}} - {\bar {\hat I}})d{\omega _1}d{\omega _2} = 0}

The transformation properties of the difference data fusion algorithm guided by integral discrete are: $D^xυφ=(j2πω1)υφ^,D^yυφ=(j2πω2)υφ^$ {\hat D}_x^\upsilon \varphi = {\left({j2\pi {\omega _1}} \right)^\upsilon}{\hat \varphi},{\hat D}_y^\upsilon \varphi = {\left({j2\pi {\omega _2}} \right)^\upsilon}{\hat \varphi}

We substitute formula (6) into formula (5) and eliminate the coefficients to obtain: $∫Ω((j2πω1)υφ^D^xυI¯|DυI|+(j2πω2)υφ^D^yυI¯|DυI|)dω1dω2−λ∫Ωφ^(I^0¯−I^¯)dω1dω2=0$ \int_\Omega {({{\left({j2\pi {\omega _1}} \right)}^\upsilon}{\hat \varphi} {{\overline {{\hat D}_x^\upsilon I}} \over {\left| {{D^\upsilon}I} \right|}} + {{\left({j2\pi {\omega _2}} \right)}^\upsilon}{\hat \varphi} {{\overline {{\hat D}_y^\upsilon I}} \over {\left| {{D^\upsilon}I} \right|}})d{\omega _1}d{\omega _2} - \lambda \int_\Omega {{\hat \varphi} (\overline {{{\hat I}_0}} - {\bar {\hat I}})d{\omega _1}d{\omega _2} = 0}}

The arbitrariness of the function φ in the differential data fusion algorithm is guided by integral discrete. We can use the basic lemma of the variational method of the differential data fusion algorithm to get: $(j2πω1)υD^xυI¯|DυI|+(j2πω2)υD^yυI¯|DυI|−λ(I^0¯−I^¯)=0$ {\left({j2\pi {\omega _1}} \right)^\upsilon}{{\overline {{\hat D}_x^\upsilon I}} \over {\left| {{D^\upsilon}I} \right|}} + {\left({j2\pi {\omega _2}} \right)^\upsilon}{{\overline {{\hat D}_y^\upsilon I}} \over {\left| {{D^\upsilon}I} \right|}} - \lambda \left({\overline {{{\hat I}_0}} - {\bar {\hat I}}} \right) = 0

We use the inverse transformation of the differential data fusion algorithm guided by integral discreteness to get the partial differential equation of the corresponding differential data fusion algorithm as: $Re{[Dxυ¯(DxυI|DυI|+Dyυ¯(DyυI|DυI|)]}−λ(I^0¯−I^¯)=0$ {\mathop{\rm Re}\nolimits} \{[\overline {D_x^\upsilon} ({{D_x^\upsilon I} \over {\left| {{D^\upsilon}I} \right|}} + \overline {D_y^\upsilon} ({{D_y^\upsilon I} \over {\left| {{D^\upsilon}I} \right|}})]\} - \lambda (\overline {{{\hat I}_0}} - {\bar {\hat I}}) = 0

Finally, the gradient descent method of the differential data fusion algorithm can be used to obtain the model of the differential data fusion algorithm based on discrete integral guidance: $∂I∂t=−Re{[Dxυ¯(DxυI|DυI|+Dyυ¯(DyυI|DυI|)]}+λ(I^0¯−I^¯)=0$ {{\partial I} \over {\partial t}} = - {\mathop{\rm Re}\nolimits} \{[\overline {D_x^\upsilon} ({{D_x^\upsilon I} \over {\left| {{D^\upsilon}I} \right|}} + \overline {D_y^\upsilon} ({{D_y^\upsilon I} \over {\left| {{D^\upsilon}I} \right|}})]\} + \lambda (\overline {{{\hat I}_0}} - {\bar {\hat I}}) = 0

Then the difference fusion of the difference data fusion algorithm guided by discrete integral guidance in each direction is defined as: $DxI(x,y)=I(x,y)−I(x−1,y)=1NI(ω1, ω2∧)(1−ej2πω1/N)ej2π(xω1+yω2)/N$ {D_x}I\left({x,y} \right) = I\left({x,y} \right) - I\left({x - 1,y} \right) = {1 \over {\sqrt N}}I(\mathop {{\omega _1},\,{\omega _2}}\limits^ \wedge)(1 - {e^{j2\pi {\omega _1}/N}}){e^{j2\pi \left({x{\omega _1} + y{\omega _2}} \right)/N}} $DyI(x,y)=I(x,y)−I(x,y−1)=1NI(ω1, ω2∧)(1−ej2πω1/N)ej2π(xω1+yω2)/N$ {D_y}I\left({x,y} \right) = I\left({x,y} \right) - I\left({x,y - 1} \right) = {1 \over {\sqrt N}}I(\mathop {{\omega _1},\,{\omega _2}}\limits^ \wedge)(1 - {e^{j2\pi {\omega _1}/N}}){e^{j2\pi \left({x{\omega _1} + y{\omega _2}} \right)/N}}

Therefore, according to the nature of the differential data fusion algorithm guided by integral discrete, the corresponding relationship between the spatial domain and the frequency domain of the first-order difference is defined as: $DxI(x,y)↔(1−e−j2πω1/N)I(ω1, ω2∧)DyI(x,y)↔(1−e−j2πω2/N)I(ω1, ω2∧)$ \matrix{{{D_x}I\left({x,y} \right) \leftrightarrow (1 - {e^{- j2\pi {\omega _1}/N}})I(\mathop {{\omega _1},\,{\omega _2}}\limits^ \wedge)} \cr {{D_y}I\left({x,y} \right) \leftrightarrow (1 - {e^{- j2\pi {\omega _2}/N}})I(\mathop {{\omega _1},\,{\omega _2}}\limits^ \wedge)} \cr}

In the same way, it can be seen that the corresponding relationship between the spatial domain and the frequency domain of the differential data fusion algorithm guided by integral discrete is: $DxnI(x,y)↔(1−e−j2πω1/N)nI(ω1, ω2∧)DynI(x,y)↔(1−e−j2πω2/N)I(ω1, ω2∧)$ \matrix{{D_x^nI(x,y) \leftrightarrow {{(1 - {e^{- j2\pi {\omega _1}/N}})}^n}I(\mathop {{\omega _1},\,{\omega _2}}\limits^ \wedge)} \cr {D_y^nI(x,y) \leftrightarrow (1 - {e^{- j2\pi {\omega _2}/N}})I(\mathop {{\omega _1},\,{\omega _2}}\limits^ \wedge)} \cr}

We extend the integer-order n to the fractional-order υ to obtain the numerical calculation formula of the differential data fusion algorithm based on discrete integral guidance: $DxυI(x,y)↔(1−e−j2πω1/N)υI(ω1, ω2∧)DyυI(x,y)↔(1−e−j2πω2/N)υI(ω1, ω2∧)$ \matrix{{D_x^\upsilon I\left({x,y} \right) \leftrightarrow {{(1 - {e^{- j2\pi {\omega _1}/N}})}^\upsilon}I(\mathop {{\omega _1},\,{\omega _2}}\limits^ \wedge)} \cr {D_y^\upsilon I\left({x,y} \right) \leftrightarrow {{(1 - {e^{- j2\pi {\omega _2}/N}})}^\upsilon}I(\mathop {{\omega _1},\,{\omega _2}}\limits^ \wedge)} \cr}

In this way, the difference data fusion algorithm guided by the integral discrete can obtain the conjugate operator of the differential operator: $DxυI(x,y)¯↔(1−e−j2πω1/N)υ¯I(ω1, ω2∧)DyυI(x,y)¯↔(1−e−j2πω2/N)υ¯I(ω1, ω2∧)$ \matrix{{\overline {D_x^\upsilon I(x,y)} \leftrightarrow \overline {{{(1 - {e^{- j2\pi {\omega _1}/N}})}^\upsilon}} I(\mathop {{\omega _1},\,{\omega _2}}\limits^ \wedge)} \cr {\overline {D_y^\upsilon I(x,y)} \leftrightarrow \overline {{{(1 - {e^{- j2\pi {\omega _2}/N}})}^\upsilon}} I(\mathop {{\omega _1},\,{\omega _2}}\limits^ \wedge)} \cr}

There is known difference data I(x, y), (x, y) ∈ Ω. Assume that the different data I(x, y) is independent of each other in the X and I(x, ·) axis directions. Therefore, only the fractional calculus numerical calculation of the difference data Y in the direction of the X axis is considered. From the G — L definition of fractional calculus, it can be seen that the fractional differential of the difference data I(x, ·) is: $aGDtυI(x,⋅)=(1h)∑j=1N−1(−1)jΓ(υ+1)Γ(j+1)Γ(υ−j+1)$ _a^GD_t^\upsilon I\left({x, \cdot} \right) = \left({{1 \over h}} \right)\sum\limits_{j = 1}^{N - 1} {{{\left({- 1} \right)}^j}{{\Gamma \left({\upsilon + 1} \right)} \over {\Gamma \left({j + 1} \right)\Gamma \left({\upsilon - j + 1} \right)}}}

We use the different data fusion algorithm guided by integral discreteness to fuse the original data in different directions to form new fused output data. This can greatly improve the difference between different data of different sensor nodes in the discrete manufacturing system [7]. The flow chart of the differential data fusion algorithm guided by integral discrete is shown in Figure 1. It can be seen from Figure 1 that the differential data fusion algorithm using discrete integral guidance first needs to integrate all the data. Then judge the difference of all the data. The integration method is used to process the different data and fuse the different data. Finally, it is judged whether the system algorithm is over according to the quality of the data fusion effect.

Differentiated data fusion under the Internet of Things based on discrete integral guidance
Internet of Things Technology

The basic characteristics of the Internet of Things technology are mainly reflected in the following aspects [8]:

(1) Comprehensive perception. Signal detection and perception are carried out through sensors, detectors, two-dimensional codes, and even transducers. This provides preconditions for intelligent analysis and network resource sharing.

(2) Reliable delivery. Through the establishment of the Internet of a Things technology platform and the integration with the Internet, the transmission of parameter information, the sharing of information resources, and real-time processing are realized.

(3) Intelligent processing. Through modern signal and information processing technology (data mining technology, cloud processing technology, neural network system technology, pattern recognition technology), information processing and analysis of massive data and extraction of useful information [9]. In this way, the object-oriented operation and control are implemented, and the user's purpose is finally achieved.

Differentiated data fusion under the Internet of Things based on discrete integral guidance

The objective function of the differentiated data fusion system under the Internet of Things based on discrete integral guidance is defined as: $aGDtυI(x)=∑j=1N−1(−1)j(υj)I(x−j)$ _a^GD_t^\upsilon I\left(x \right) = \sum\limits_{j = 1}^{N - 1} {{{\left({- 1} \right)}^j}\left({\matrix{\upsilon \cr j \cr}} \right)I\left({x - j} \right)}

Assume that the differentiated data fusion function Cυ(x) satisfies: $Cυ(x)={(−1)x(υx),x≥00,x<0$ {C^{\upsilon \left(x \right)}} = \left\{{\matrix{{{{\left({- 1} \right)}^x}\left({\matrix{\upsilon \cr x \cr}} \right),} & {x \ge 0} \cr {0,} & {x < 0} \cr}} \right.

Therefore, the system of differentiated data fusion can be expressed as: $aGDtυI(x)=Cυ(x)*I(x)$ _a^GD_t^\upsilon I\left(x \right) = {C^{\upsilon \left(x \right)}}*I\left(x \right)

So we use the function of the BVυ(Ω) space of differentiated data fusion to obtain the differentiated data fusion under the Internet of Things based on discrete integral guidance as: $E(I)=∫Ω|cυ*I|dxdy+λ2|I0−I|L22$ E\left(I \right) = \int_\Omega {\left| {{c^\upsilon}*I} \right|dxdy + {\lambda \over 2}\left| {{I_0} - I} \right|_{{L_2}}^2}

In: ${|cυ*I|=(cυ*I)x2+(cυ*I)y2(cυ*I)x=∫Ωcυ(z)I(x−z,y)dz(cυ*I)y=∫Ωcυ(z)I(x,y−z)dz$ \left\{{\matrix{{\left| {{c^\upsilon}*I} \right| = \sqrt {\left({{c^\upsilon}*I} \right)_x^2 + \left({{c^\upsilon}*I} \right)_y^2}} \hfill \cr {{{\left({{c^\upsilon}*I} \right)}_x} = \int_\Omega {{c^{\upsilon \left(z \right)}}} I\left({x - z,y} \right)dz} \hfill \cr {{{\left({{c^\upsilon}*I} \right)}_y} = \int_\Omega {{c^{\upsilon \left(z \right)}}} I\left({x,y - z} \right)dz} \hfill \cr}} \right.

We get the expression of the differentiated data. It satisfies the following formula: $g(ε)=E(I+εφ)=∫Ω|cυ(I+εφ)|dxdy+λ2|I0−I+εφ|L22$ g\left(\varepsilon \right) = E\left({I + \varepsilon \varphi} \right) = \int_\Omega {\left| {{c^\upsilon}\left({I + \varepsilon \varphi} \right)} \right|dxdy + {\lambda \over 2}\left| {{I_0} - I + \varepsilon \varphi} \right|_{{L_2}}^2}

We still use the basic properties of the functional extremum. Let g′(0) = 0 obtain: $∫Ω(cυ*I)x(cυ*φ)x+(cυ*I)y(cυ*φ)y|cυ*I|dxdy−∫Ω(I0−I)φdxdy=0$ \int_\Omega {{{{{\left({{c^\upsilon}*I} \right)}_x}{{\left({{c^\upsilon}*\varphi} \right)}_x} + {{\left({{c^\upsilon}*I} \right)}_y}{{\left({{c^\upsilon}*\varphi} \right)}_y}} \over {\left| {{c^\upsilon}*I} \right|}}} dxdy - \int_\Omega {\left({{I_0} - I} \right)\varphi dxdy = 0}

Because when the differentiated data in the system (x, y) ∉ R is I(x, y) =0. So when Ω → R2 is: $∫R2fgdxdy=∫R2f^g^¯dω1dω2$ \int_{{R^2}} {fgdxdy = \int_{{R^2}} {\overline {{\hat f}{\hat g}} d{\omega _1}d{\omega _2}}}

According to the differential data equation, the final transformation form of the objective function of the differential data fusion system under the Internet of Things guided by integral discreteness can be obtained as: $12π∫Ω((cυ*^I)x¯|cu*I|)(cυ*^φ)xdω1dω2+12π∫Ω((cυ*^I)y¯|cu*I|)(cυ*^φ)ydω1dω2−λ12π∫Ω(I^¯0−I^¯)φ^dω1dω2=0$ \matrix{{{1 \over {2\pi}}\int_\Omega {\left({{{\overline {{{\left({{c^\upsilon}{\hat *I}} \right)}_x}}} \over {\left| {{c^u}*I} \right|}}} \right)} {{\left({{c^\upsilon}{\hat *\varphi}} \right)}_x}d{\omega _1}d{\omega _2} +} \hfill \cr {{1 \over {2\pi}}\int_\Omega {\left({{{\overline {{{\left({{c^\upsilon}{\hat *I}} \right)}_y}}} \over {\left| {{c^u}*I} \right|}}} \right)} {{\left({{c^\upsilon}{\hat *\varphi}} \right)}_y}d{\omega _1}d{\omega _2} -} \hfill \cr {\lambda {1 \over {2\pi}}\int_\Omega {\left({{{\bar {\hat I}}_0} - \bar {\hat I}} \right)} {{\hat \varphi}} d{\omega _1}d{\omega _2} = 0} \hfill \cr}

The differentiated data fusion algorithm under the Internet of Things guided by integral discreteness can continuously collect data information in the Internet of Things system. It merges the differences of the differentiated data [10].

System experiment and result analysis
Description of the experimental environment

The hardware equipment used in the experiment is brand Dell, and the software environment is IntelPentiumE2180 @ 4GHzCPU / 2.00GB / Windows7. The article tests differentiated data fusion algorithms’ performance pros and cons based on discrete integral guidance under the Internet of Things. We use Matlab simulation software to build an experimental environment [11]. The article uses a set of 100 random difference data to conduct a system experiment. The detailed experimental parameters are shown in Table 1.

Description of experimental parameters.

Project Parameter Description
Number of difference data nodes 100
Number of different data types 6
Differential data distribution type Random distribution difference
Difference tolerance Within the set range, a standard deviation of 1
Difference processing method Equal treatment
Result analysis

The system experiment is carried out under the system experiment environment constructed in Table 1. The distribution of the original data is shown in Figure 2.

It can be seen from Figure 2 that the data of each discrete manufacturing system in the original state presents the characteristics of the individual combination. It shows strong clustering nder the same rule [12]. The article uses a differentiated data fusion algorithm based on discrete integral guidance to process the above data under the Internet of Things. The result is shown in Figure 3.

Through the comparison of Figure 2 and Figure 3, it can be seen that the original data has obvious partition characteristics due to the differences in equipment and sources [13]. We use a differentiated data fusion algorithm under the Internet of Things based on discrete integral guidance to process the data, and the data distribution characteristics are more random. The data spectrum before and after the differential data fusion is shown in Figure 4.

It can be seen from Figure 4 that the spectral characteristics of the original data show a situation where six peaks are merged. The original data distribution is relatively regular, so the data peak characteristic is very strong. After the differential fusion algorithm processes the data, the data spectrum becomes a uniformly distributed random spectrum. This shows that the differences between the data have been merged.

Conclusion

A discrete system differential data fusion in the Internet of Things guided by integral discrete is studied. The data of each node needs to be processed separately. This article proposes a discrete system differential data fusion in the Internet of Things guided by integral discrete. Then treat all data as research objects for unified processing. Then, the method of discrete integral guidance is used to process all the obtained differential data. We integrate the data we have to judge the differences of all the data. We use the integration method to process the different data and fuse the different data to combine effectively. Finally, a set of 6 types of data of 100 nodes is used for experiments. The results show that the discrete system differential data fusion in the Internet of Things is guided by integral discreteness and the average distribution of the data spectrum. So the algorithm has a very good application value.

#### Description of experimental parameters.

Project Parameter Description
Number of difference data nodes 100
Number of different data types 6
Differential data distribution type Random distribution difference
Difference tolerance Within the set range, a standard deviation of 1
Difference processing method Equal treatment

Hui, H., Zhou, C., Xu, S., & Lin, F. A novel secure data transmission scheme in industrial Internet of things. China Communications., 2020; 17(1):73–88 HuiH. ZhouC. XuS. LinF. A novel secure data transmission scheme in industrial Internet of things China Communications. 2020 17 1 73 88 10.23919/JCC.2020.01.006 Search in Google Scholar

Nuryani, D., Rusyaman, E., & Subartini, B. Convergence Analysis from the Solution of Riccati’s Fractional Differential Equation by Using Polynomial Least Squares Method. Eksakta: Berkala Ilmiah Bidang MIPA (E-ISSN: 2549-7464)., 2020; 21(1):7–14 NuryaniD. RusyamanE. SubartiniB. Convergence Analysis from the Solution of Riccati’s Fractional Differential Equation by Using Polynomial Least Squares Method Eksakta: Berkala Ilmiah Bidang MIPA (E-ISSN: 2549-7464). 2020 21 1 7 14 10.24036/eksakta/vol21-iss1/211 Search in Google Scholar

Rahaman, H., Kamrul Hasan, M., Ali, A. & Shamsul Alam, M. Implicit Methods for Numerical Solution of Singular Initial Value Problems. Applied Mathematics and Nonlinear Sciences., 2021; 6(1): 1–8 RahamanH. Kamrul HasanM. AliA. Shamsul AlamM. Implicit Methods for Numerical Solution of Singular Initial Value Problems Applied Mathematics and Nonlinear Sciences. 2021 6 1 1 8 10.2478/amns.2020.2.00001 Search in Google Scholar

Vanli, A., Ünal, I. & Özdemir, D. Normal complex contact metric manifolds admitting a semi symmetric metric connection. Applied Mathematics and Nonlinear Sciences., 2020; 5(2): 49–66 VanliA. ÜnalI. ÖzdemirD. Normal complex contact metric manifolds admitting a semi symmetric metric connection Applied Mathematics and Nonlinear Sciences. 2020 5 2 49 66 10.2478/amns.2020.2.00013 Search in Google Scholar

Wu, S. Research on the application of spatial partial differential equation in user oriented information mining. Alexandria Engineering Journal., 2020; 59(4):2193–2199 WuS. Research on the application of spatial partial differential equation in user oriented information mining Alexandria Engineering Journal. 2020 59 4 2193 2199 10.1016/j.aej.2020.01.047 Search in Google Scholar

Abd El-Latif, A. A., Abd-El-Atty, B., Mazurczyk, W., Fung, C., & Venegas-Andraca, S. E. Secure data encryption based on quantum walks for 5G Internet of Things scenario. IEEE Transactions on Network and Service Management., 2020; 17(1):118–131 Abd El-LatifA. A. Abd-El-AttyB. MazurczykW. FungC. Venegas-AndracaS. E. Secure data encryption based on quantum walks for 5G Internet of Things scenario IEEE Transactions on Network and Service Management. 2020 17 1 118 131 10.1109/TNSM.2020.2969863 Search in Google Scholar

Park, C., Khater, M. M., Abdel-Aty, A. H., Attia, R. A., Rezazadeh, H., Zidan, A. M., & Mohamed, A. B. Dynamical analysis of the nonlinear complex fractional emerging telecommunication model with higher–order dispersive cubic–quintic. Alexandria Engineering Journal., 2020; 59(3):1425–1433 ParkC. KhaterM. M. Abdel-AtyA. H. AttiaR. A. RezazadehH. ZidanA. M. MohamedA. B. Dynamical analysis of the nonlinear complex fractional emerging telecommunication model with higher–order dispersive cubic–quintic Alexandria Engineering Journal. 2020 59 3 1425 1433 10.1016/j.aej.2020.03.046 Search in Google Scholar

Jha, S., Nkenyereye, L., Joshi, G. P., & Yang, E. Mitigating and monitoring smart city using Internet of things. Computers, Materials & Continua., 2020; 65(2):1059–1079 JhaS. NkenyereyeL. JoshiG. P. YangE. Mitigating and monitoring smart city using Internet of things Computers, Materials & Continua. 2020 65 2 1059 1079 10.32604/cmc.2020.011754 Search in Google Scholar

Liu, S., Zhang, Y., Xu, L., Ding, F., Alsaedi, A., & Hayat, T. Extended gradient-based iterative algorithm for bilinear state-space systems with moving average noises by using the filtering technique. International Journal of Control, Automation and Systems., 2021; 19(4):1597–1606 LiuS. ZhangY. XuL. DingF. AlsaediA. HayatT. Extended gradient-based iterative algorithm for bilinear state-space systems with moving average noises by using the filtering technique International Journal of Control, Automation and Systems. 2021 19 4 1597 1606 10.1007/s12555-019-0831-9 Search in Google Scholar

Cai, W., Wen, X., & Tu, Q. Designing an intelligent greenhouse monitoring system based on the Internet of Things. Applied Ecology and Environmental Research., 2019; 17(4):8449–8464 CaiW. WenX. TuQ. Designing an intelligent greenhouse monitoring system based on the Internet of Things Applied Ecology and Environmental Research. 2019 17 4 8449 8464 10.15666/aeer/1704_84498464 Search in Google Scholar

Mursi, K. T., & Zhuang, Y. Experimental Study of Component-Differentially-Challenged XOR PUFs as Security Primitives for Internet-of-Things. J. Commun., 2020; 15(10):714–721 MursiK. T. ZhuangY. Experimental Study of Component-Differentially-Challenged XOR PUFs as Security Primitives for Internet-of-Things J. Commun. 2020 15 10 714 721 10.12720/jcm.15.10.714-721 Search in Google Scholar

Yang, H., Kumara, S., Bukkapatnam, S. T., & Tsung, F. The internet of things for smart manufacturing: A review. IISE Transactions., 2019; 51(11):1190–1216 YangH. KumaraS. BukkapatnamS. T. TsungF. The internet of things for smart manufacturing: A review IISE Transactions. 2019 51 11 1190 1216 10.1080/24725854.2018.1555383 Search in Google Scholar

Cui, T., Ding, F., Jin, X. B., Alsaedi, A., & Hayat, T. Joint multi-innovation recursive extended least squares parameter and state estimation for a class of state-space systems. International Journal of Control, Automation and Systems., 2020; 18(6):1412–1424 CuiT. DingF. JinX. B. AlsaediA. HayatT. Joint multi-innovation recursive extended least squares parameter and state estimation for a class of state-space systems International Journal of Control, Automation and Systems. 2020 18 6 1412 1424 10.1007/s12555-019-0053-1 Search in Google Scholar

Empfohlene Artikel von Trend MD