Analysis of Homotopy Perturbation Method for Solving Fractional Order Differential Equations

The analysis of Homotopy Perturbation Method (HPM) for the solution of fractional partial differential equations (FPDEs) is presented. A unified convergence theorem is given. In order to validate the theory, the solution of fractional-order Burger-Poisson (FBP) equation is obtained. Furthermore, thi...

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Bibliographic Details
Published in:Mathematics (Basel) 2019-01, Vol.7 (1), p.40
Main Authors: Javeed, Shumaila, Baleanu, Dumitru, Waheed, Asif, Shaukat Khan, Mansoor, Affan, Hira
Format: Article
Language:English
Subjects:
Boundary value problems
Burger-Poisson equation of fractional order
Differential equations
fractional derivatives
HPM
Mathematical analysis
Mathematics
Partial differential equations
Perturbation methods
Wireless networks
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Summary:The analysis of Homotopy Perturbation Method (HPM) for the solution of fractional partial differential equations (FPDEs) is presented. A unified convergence theorem is given. In order to validate the theory, the solution of fractional-order Burger-Poisson (FBP) equation is obtained. Furthermore, this work presents the method to find the solution of FPDEs, while the same partial differential equation (PDE) with ordinary derivative i.e., for α = 1 , is not defined in the given domain. Moreover, HPM is applied to a complicated obstacle boundary value problem (BVP) of fractional order.
ISSN:2227-7390
2227-7390
DOI:10.3390/math7010040