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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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\textit{O. Abdulaziz} et al., Differ. Equ. Nonlinear Mech. 2008, Article ID 686512, 16 p. (2008; Zbl 1172.35305)

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