Analysis of the Time Fractional-Order Coupled Burgers Equations with Non-Singular Kernel Operators

Aljahdaly, Noufe H.; Agarwal, Ravi P.; Shah, Rasool; Botmart, Thongchai

doi:10.3390/math9182326

Cited by 41 publications

(20 citation statements)

References 30 publications

(28 reference statements)

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“…The designed SCGNNs scheme can be applied in the future to solve the various fluid systems, lonngren-wave networks [35][36][37], fractional models [38][39][40][41][42], delayed neural networks [43][44][45][46] and nonlinear models [47][48][49][50].…”

Section: Discussionmentioning

confidence: 99%

Computational Stochastic Investigations for the Socio-Ecological Dynamics with Reef Ecosystems

Botmart¹,

Sabir²,

Alwabli³

et al. 2022

Computers, Materials &Amp; Continua

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The motive of this work is to present a computational design using the stochastic scaled conjugate gradient (SCG) neural networks (NNs) called as SCGNNs for the socio-ecological dynamics (SED) with reef ecosystems and conservation estimation. The mathematical descriptions of the SED model are provided that is dependent upon five categories, macroalgae M(v), breathing coral C(v), algal turf T(v), the density of parrotfish P(v) and the opinion of human opinion X (v). The stochastic SCGNNs process is applied to formulate the SED model based on the sample statistics, testing, accreditation and training. Three different variations of the SED have been provided to authenticate the stochastic SCGNNs performance through the statics for training, accreditation, and testing are 77%, 12% and 11%, respectively. The obtained numerical performances have been compared with the Runge-Kutta approach to solve the SED model. The reduction of mean square error (MSE) is used to investigate the numerical measures through the SCGNNs for solving the SED model. The precision of the SCGNNs is validated through the comparison of the results and the absolute error performances. The reliability of the SCGNNs is performed by using the correlation values, state transitions (STs), error histograms (EHs), MSE measures and regression analysis.

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Section: Discussionmentioning

confidence: 99%

Computational Stochastic Investigations for the Socio-Ecological Dynamics with Reef Ecosystems

Botmart¹,

Sabir²,

Alwabli³

et al. 2022

Computers, Materials &Amp; Continua

Self Cite

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“…For these complex problems, a new technique has been used by the researchers known as fractional differential equations (FDEs). In the mathematical modeling of realworld physical problems, FDEs have been widespread due to their numerous applications in engineering and real-life sciences problems [6][7][8][9], such as economics [10], solid mechanics [11], continuum and statistical mechanics [12], oscillation of earthquakes [13], dynamics of interfaces between soft-nanoparticles and rough substrates [14], fluiddynamic traffic model [15], colored noise [16], solid mechanics [11], anomalous transport [17], and bioengineering [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Analysis of the Fractional‐Order Delay Differential Equations by the Numerical Method

et al. 2022

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In this study, we implemented a new numerical method known as the Chebyshev Pseudospectral method for solving nonlinear delay differential equations having fractional order. The fractional derivative is defined in Caputo manner. The proposed method is simple, effective, and straightforward as compared to other numerical techniques. To check the validity and accuracy of the proposed method, some illustrative examples are solved by using the present scenario. The obtained results have confirmed the greater accuracy than the modified Laguerre wavelet method, the Chebyshev wavelet method, and the modified wavelet-based algorithm. Moreover, based on the novelty and scientific importance, the present method can be extended to solve other nonlinear fractional-order delay differential equations.

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“…To find the solution of FPDEs is a hard task, however, many mathematicians devoted their sincere work and developed numerical and analytical techniques to solve FPDEs. Some of these techniques include homotopy analysis method (HAM) [22], operational matrix [23], Adomian decomposition method (ADM) [24], homotopy perturbation method (HPM) [25], meshless method [26], variational iteration method (VIM) [27], tau method [28], Bernstein polynomials [29], the Haar wavelet method [30], the Laplace transform method [31], the Legendre base method [32],…”

Section: Introductionmentioning

confidence: 99%

Fractional Analysis of Coupled Burgers Equations within Yang Caputo-Fabrizio Operator

Shah

El‐Zahar

Chung

2022

Journal of Function Spaces

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This work applies a novel analytical technique to the fractional view analysis of coupled Burgers equations. The proposed problems have been fractionally analyzed in the Caputo-Fabrizio sense. The Yang transformation was initially applied to the specified problem in the current approach. The series form solution is then obtained using the Adomian decomposition technique. The desired analytical solution is obtained after performing the inverse transform. Specific examples of fractional Burgers couple systems are used to validate the proposed technique. The current strategy has been found to be a useful methodology with a close match to actual solutions. The proposed method offers a lower computing cost and a faster convergence rate. As a result, the suggested technique can be applied to a variety of fractional order problems.

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Analysis of the Time Fractional-Order Coupled Burgers Equations with Non-Singular Kernel Operators

Cited by 41 publications

References 30 publications

Computational Stochastic Investigations for the Socio-Ecological Dynamics with Reef Ecosystems

Computational Stochastic Investigations for the Socio-Ecological Dynamics with Reef Ecosystems

Analysis of the Fractional‐Order Delay Differential Equations by the Numerical Method

Fractional Analysis of Coupled Burgers Equations within Yang Caputo-Fabrizio Operator

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