WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - WoS: 4Citation - Scopus: 4Double-Quasi 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) Pandey, Prashant; Gomez-Aguilar, J. F.; Baleanu, D.; Kumar, SachinOur 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.Article Citation - WoS: 66Citation - Scopus: 77Numerical Approach of Fokker-Planck Equation With Caputo-Fabrizio Fractional Derivative Using Ritz Approximation(Elsevier, 2018) Jafari, H.; Lia, A.; Baleanu, D.; Firoozjaee, M. A.In this manuscript, a type of Fokker-Planck equation (FPE) with Caputo-Fabrizio fractional derivative is considered. We present a numerical approach which is based on the Ritz method with known basis functions to transform this equation into an optimization problem. It leads to a nonlinear algebraic system. Then, we obtain the coefficients of basis functions by solving the algebraic system. The convergence of this technique is discussed extensively. Three examples are included to show the applicability and validity of this method. (C) 2017 Elsevier B.V. All rights reserved.