An Analytical and Approximate Solution for Nonlinear Volterra Partial Integro-Differential Equations with a Weakly Singular Kernel Using the Fractional Differential Transform Method

Abstract EN

An analytical-approximate method is proposed for a type of nonlinear Volterra partial integro-differential equations with a weakly singular kernel.

This method is based on the fractional differential transform method (FDTM).

The approximate solutions of these equations are calculated in the form of a finite series with easily computable terms.

The analytic solution is represented by an infinite series.

We state and prove a theorem regarding an integral equation with a weak kernel by using the fractional differential transform method.

The result of the theorem will be used to solve a weakly singular Volterra integral equation later on.