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Homotopy analysis method for solving a class of fractional partial differential equations. (English) Zbl 1222.65109

Summary: 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 \(\hbar\) on the convergence of the approximate solution. Also, they illustrate the effect of the fractional derivative orders \(\alpha \) and \(\beta \) on the solution behavior.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35L45 Initial value problems for first-order hyperbolic systems
35R11 Fractional partial differential equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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