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

Ahmen Hamoud, Kirtiwant Ghadle


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.


Homotopy analysis method; Caputo fractional derivative; fractional Volterra-Fredholm integro-differential equation; existence and uniqueness results.

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