Usage of the homotopy analysis method for solving fractional Volterra-Fredholm integro-differential equation of the second kind

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Published: Dec 25, 2018
DOI: https://doi.org/10.5556/j.tkjm.49.2018.2718
Keywords:
Homotopy analysis method Caputo fractional derivative fractional Volterra-Fredholm integro-differential equation existence and uniqueness results.

Main Article Content

Ahmen Hamoud
Kirtiwant Ghadle

Abstract

The reliability of the homotopy analysis method (HAM) and reduction in the size of the computational work give this method a wider applicability. In this paper, HAM has been successfully applied to find the approximate solutions of Caputo fractional Volterra-Fredholm integro-differential equations. Also, the behavior of the solution can be formally determined by analytical approximation. Moreover, the study proves the existence and uniqueness results and the convergence of the solution. This paper concludes with an example to demonstrate the validity and applicability of the proposed technique.

Article Details

How to Cite
Hamoud, A., & Ghadle, K. (2018). Usage of the homotopy analysis method for solving fractional Volterra-Fredholm integro-differential equation of the second kind. Tamkang Journal of Mathematics, 49(4), 301–315. https://doi.org/10.5556/j.tkjm.49.2018.2718
Issue
Vol. 49 No. 4 (2018)
Section
Papers
Author Biographies

Ahmen Hamoud

Department of Mathematics, Dr.Babasaheb AmbedkarMarathwada University, Aurangabad, 431004, India.

Kirtiwant Ghadle

Department ofMathematics, Dr.Babasaheb AmbedkarMarathwada University, Aurangabad, 431004, India.

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