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Series solutions of time-fractional PDEs by homotopy analysis method. (English) Zbl 1172.35305

Summary: The homotopy analysis method (HAM) is applied to solve linear and nonlinear fractional partial differential equations (fPDEs). The fractional derivatives are described by Caputo’s sense. Series solutions of the fPDEs are obtained. A convergence theorem for the series solution is also given. The test examples, which include a variable coefficient, inhomogeneous and hyperbolic-type equations, demonstrate the capability of HAM for nonlinear fPDEs.

MSC:

35A25 Other special methods applied to PDEs
26A33 Fractional derivatives and integrals
35C10 Series solutions to PDEs
35S05 Pseudodifferential operators as generalizations of partial differential operators

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