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Browsing by Author "Pandey, Prashant"

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    Article
    Citation - WoS: 39
    Citation - Scopus: 46
    An efficient technique for solving the space-time fractional reaction-diffusion equation in porous media
    (Elsevier, 2020) Pandey, Prashant; Baleanu, Dumitru; Kumar, Sachin; Gomez-Aguilar, J. F.; Baleanu, D.; 56389; Matematik
    In this paper, we obtained the approximate numerical solution of space-time fractional-order reaction-diffusion equation using an efficient technique homotopy perturbation technique using Laplace transform method with fractional-order derivatives in Caputo sense. The solution obtained is very useful and significant to analyze the many physical phenomenons. The present technique demonstrates the coupling of the homotopy perturbation technique and Laplace transform using He's polynomials for finding the numerical solution of various non-linear fractional complex models. The salient features of the present work are the graphical presentations of the approximate solution of the considered porous media equation for different particular cases and reflecting the presence of reaction terms presented in the equation on the physical behavior of the solute profile for various particular cases.
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    Article
    Citation - WoS: 2
    Citation - Scopus: 2
    DOUBLE-QUASI-WAVELET NUMERICAL METHOD FOR THE VARIABLE-ORDER TIME FRACTIONAL AND RIESZ SPACE FRACTIONAL REACTION-DIFFUSION EQUATION INVOLVING DERIVATIVES IN CAPUTO-FABRIZIO SENSE
    (World Scientific Publ Co Pte Ltd, 2020) Kumar, Sachin; Baleanu, Dumitru; Pandey, Prashant; Gomez-Aguilar, J. F.; Baleanu, D.; 56389; Matematik
    Our motive in this scientific contribution is to deal with nonlinear reaction-diffusion equation having both space and time variable order. The fractional derivatives which are used are non-singular having exponential kernel. These derivatives are also known as Caputo-Fabrizio derivatives. In our model, time fractional derivative is Caputo type while spatial derivative is variable-order Riesz fractional type. To approximate the variable-order time fractional derivative, we used a difference scheme based upon the Taylor series formula. While approximating the variable order spatial derivatives, we apply the quasi-wavelet-based numerical method. Here, double-quasi-wavelet numerical method is used to investigate this type of model. The discretization of boundary conditions with the help of quasi-wavelet is discussed. We have depicted the efficiency and accuracy of this method by solving the some particular cases of our model. The error tables and graphs clearly show that our method has desired accuracy.