Approximate Solution of Nonlinear Fractional Integro-Differential Equations of the Volterra Fredhlom-Hammerstein Type by using Modified Laplace Adomian Decomposition Method - Hamood, Maha M.; Sharif, Abdulrahman A.; Ghadle, Kirtiwant P. (Discontinuity, Nonlinearity, and Complexity, 2026)
In this study, we will formulate semianalytic solutions to nonlinear integro-fractional differential equations of the Volterra Fredhlom-Hammerstein type using a different kernel and a combination of the Laplace transform and the Modified Adomian Decomposition Method. The kernels in this case are the difference kernel and the first-order simple degenerate kernel. We describe the higher-multifractal derivative in the Caputo sense. These approaches conceptualise the solution to a functional equation as an infinite series of components that converge to the solution upon applying the inverse of the Laplace transformation. Numerical calculations typically use a reduced number of terms when obtaining a closed-form solution is not possible. Finally, examples demonstrate these points.