A new analyzing technique for nonlinear time fractional Cauchy reaction-diffusion model equations

In this article, analytical exact and approximate solutions for fractional physical equations are obtained successfully via efficient analytical method called fractional residual power series method (FRPSM). The fractional derivatives are described in the Caputo sense. Three applications are discussed, showing the validity, accuracy and efficiency of the present method. The solution via FRPSM shows excellent agreement in comparison with the solutions obtained from other established methods. Also, the FRPSM can be used to solve other nonlinear fractional partial differential equation problems. The final results are presented in graphs and tables, which show the effectiveness, quality and strength of the presented method.

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“…The basic definitions, properties and advantages of the residual power series method are given in ref. [12][13][14][15][16].…”

Section: Proposed Methodsmentioning

confidence: 99%

Fractional residual power series method for the analytical and approximate studies of fractional physical phenomena

Ismail

Abdl-Rahim²,

Ahmad

et al. 2020

Open Physics

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“…The approximate solution of Equation has been obtained by various analytical approaches, such as Hamilton principle, 4,5 Homotopy perturbation transform method, 6–9 Haar wavelet method, 10 Variational iteration algorithm method, 11–18 , 19–29 It is important to note that the foam drainage equation will be subjected to gravity and Equation will not describe the complex motion under microgravity 30–32 …”

Section: Introductionmentioning

confidence: 99%

A study of the fractal foam drainage model in a microgravity space

Wang

2021

Math Methods in App Sciences

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The foam drainage mainly depends on the influence of gravity and foam surface tension. In this work, we consider the foam drainage in a microgravity condition, and its fractal modification is established by using the fractal derivative. The variational principle of the novel fractal model is successfully obtained by the semi‐inverse method. Finally, an analytical solution is obtained by the variational iteration method; the effect of the fractal order on the solution property is illustrated.

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“…Many physicists and mathematicians have focused their attention on formulating some nonlinear phenomena to demonstrate their characterization of undiscovered models [12][13][14]. Deriving accurate analytical, semianalytical, approximate techniques has taken more attention of many researchers; consequently, many distinct techniques have been derived, such as [15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Five semi analytical and numerical simulations for the fractional nonlinear space-time telegraph equation

et al. 2021

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The accuracy of analytical obtained solutions of the fractional nonlinear space–time telegraph equation that has been constructed in (Hamed and Khater in J. Math., 2020) is checked through five recent semi-analytical and numerical techniques. Adomian decomposition (AD), El Kalla (EK), cubic B-spline (CBS), extended cubic B-spline (ECBS), and exponential cubic B-spline (ExCBS) schemes are used to explain the matching between analytical and approximate solutions, which shows the accuracy of constructed traveling wave solutions. In 1880, Oliver Heaviside derived the considered model to describe the cutting-edge or voltage of an electrified transmission. The matching between solutions has been explained by plotting them in some different sketches.

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A new analyzing technique for nonlinear time fractional Cauchy reaction-diffusion model equations

Cited by 100 publications

References 35 publications

Fractional residual power series method for the analytical and approximate studies of fractional physical phenomena

Fractional residual power series method for the analytical and approximate studies of fractional physical phenomena

A study of the fractal foam drainage model in a microgravity space

Five semi analytical and numerical simulations for the fractional nonlinear space-time telegraph equation

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