Physics

Nonlinear system

Pure mathematics

Volterra integral equation

Uniqueness

Volterra equations

Mathematics

Mathematical analysis

Integral equation

Quantum mechanics

Differential equation

Applied mathematics

International Journal of Apllied Mathematics

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.

EXISTENCE AND UNIQUENESS THEOREMS FOR FRACTIONAL VOLTERRA-FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS