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: 4On the Approximate Solution of Fractional-Order Whitham-Broer Equations(World Scientific Publ Co Pte Ltd, 2021) Gomez-Aguilar, J. F.; Alderremy, A. A.; Aly, Shaban; Baleanu, Dumitru; Khan, HassanIn this paper, the Homotopy perturbation Laplace method is implemented to investigate the solution of fractional-order Whitham-Broer-Kaup equations. The derivative of fractional-order is described in Caputo's sense. To show the reliability of the suggested method, the solution of certain illustrative examples are presented. The results of the suggested method are shown and explained with the help of its graphical representation. The solutions of fractional-order problems as well as integer-order problems are determined by using the present technique. It has been observed that the obtained solutions are in significant agreement with the actual solutions to the targeted problems. Computationally, it has been analyzed that the solutions at different fractional-orders have a higher rate of convergence to the solution at integer-order of the derivative. Due to the analytical analysis of the problems, this study can further modify the solution of other fractional-order problems.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.