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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Said Mesloub & Saleem Obaidat, 2019. "Homotopy Analysis Method for a Fractional Order Equation with Dirichlet and Non-Local Integral Conditions," Mathematics, MDPI, vol. 7(12), pages 1-18, December.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:12:p:1167-:d:293290
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