Homotopy Analysis Method for a Fractional Order Equation with Dirichlet and Non-Local Integral Conditions

Said Mesloub and Saleem Obaidat
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Said Mesloub: Mathematics Department, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Saleem Obaidat: Mathematics Department, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Mathematics, 2019, vol. 7, issue 12, 1-18

Abstract: The main purpose of this paper is to obtain some numerical results via the homotopy analysis method for an initial-boundary value problem for a fractional order diffusion equation with a non-local constraint of integral type. Some examples are provided to illustrate the efficiency of the homotopy analysis method (HAM) in solving non-local time-fractional order initial-boundary value problems. We also give some improvements for the proof of the existence and uniqueness of the solution in a fractional Sobolev space.

Keywords: BIVP; weighted non-local conditions; parabolic fractional differential equation; homotpy method; numerical solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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