Analysis of Homotopy Perturbation Method for Solving Fractional Order Differential Equations

Shumaila Javeed, Dumitru Baleanu, Asif Waheed, Mansoor Shaukat Khan and Hira Affan
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Shumaila Javeed: Department of Mathematics, COMSATS University Islamabad, Park Road, 45550 Chak Shahzad Islamabad, Pakistan
Dumitru Baleanu: Department of Mathematics, Cankaya University, 06790 Ankara, Turkey
Asif Waheed: Department of Mathematics, COMSATS University Islamabad, Kamra Rd, Attock, Punjab 43600, Pakistan
Mansoor Shaukat Khan: Department of Mathematics, COMSATS University Islamabad, Park Road, 45550 Chak Shahzad Islamabad, Pakistan
Hira Affan: Department of Physics, COMSATS University Islamabad, Park Road, 45550 Chak Shahzad Islamabad, Pakistan

Mathematics, 2019, vol. 7, issue 1, 1-14

Abstract: 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.

Keywords: Burger-Poisson equation of fractional order; HPM; fractional derivatives (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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