EXISTENCE AND UNIQUENESS THEOREMS
FOR FRACTIONAL VOLTERRA-FREDHOLM
Ahmed A. Hamoud1, Kirtiwant P. Ghadle2,
M.Sh. Bani Issa3, Giniswamy4 1,2Department of Mathematics
Dr. Babasaheb Ambedkar Marathwada University
Aurangabad, 431004, INDIA 3,4Department of Mathematics
P.E.T. Research Foundation
Mandya, University of Mysore, 570401, INDIA
In this article, the homotopy perturbation method has been successfully applied to find the approximate solution of a Caputo fractional Volterra-Fredholm integro-differential equation. The reliability of the method and reduction in the size of the computational work give this method a wider applicability. Also, the behavior of the solution can be formally determined by the analytical approximate. Moreover, we proved the existence and uniqueness results of the solution. Finally, an example is included to demonstrate the validity and applicability of the proposed technique.
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