Modified Laplace decomposition method for fractional Volterra-Fredholm integro-differential equations

This paper successfully applies the Adomian decomposition  and the modified Laplace Adomian decomposition methods to find  the approximate solution of a nonlinear fractional Volterra-Fredholm integro-differential equation. The reliability of the methods and reduction in the size of the computational work give these methods a wider applicability. Also, the behavior of the solution can be formally determined by analytical approximate.  Moreover, the paper proves the convergence and uniqueness of the solution. Finally, this study includes an example to demonstrate the validity and applicability of the proposed techniques.

Keywords:

Laplace transform , Adomian decomposition method , fractional Volterra-Fredholm integro-differential equation , Caputo fractional derivative