A Novel Approach to Solve Nonlinear Higher Order Fractional Volterra–Fredholm Integro-Differential Equations Using Laplace Adomian Decomposition Method

Abstract

This research will integrate the Laplace transform method with the Adomian Decomposition Method to semi-analytically treat nonlinear integro-fractional differential equations of the Volterra–Fredholm–Hammerstein type. The higher-order fractional derivative will be expressed in the Caputo sense, and the first-order simple degenerate and the difference kernel will be used. With this approach, the inverse Laplace transform is applied, and the solution of the equation is viewed as the sum of an endless series of components that usually converge to the solution. Numerical applications frequently employ a shortened number of terms when a closed-form solution is not possible. Lastly, a diagram displaying the arrived at and discussed solutions was shown along with illustrative examples.