Homotopy analysis method for solving a class of fractional partial differential equations |
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| Institution: | 1. Department of Mathematics and Statistics, University of Victoria, British Columbia V8W 3R4, Canada;2. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan, Republic of China;3. Department of Mathematics, JECRC University, Jaipur 303905, Rajasthan, India |
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| Abstract: | In this paper, the homotopy analysis method is applied to obtain the solution of fractional partial differential equations with spatial and temporal fractional derivatives in Riesz and Caputo senses, respectively. Some properties of Riesz fractional derivative utilized in obtaining the series solution are proved. Numerical examples demonstrate the effect of changing homotopy auxiliary parameter ℏ on the convergence of the approximate solution. Also, they illustrate the effect of the fractional derivative orders α and β on the solution behavior. |
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