Laplace Adomian and Laplace Modified Adomian Decomposition Methods for Solving Nonlinear Integro-Fractional Differential Equations of the Volterra-Hammerstein Type


In this work, we will combine the Laplace transform method with the Adomiandecomposition method and modified Adomian decomposition method for semianalytictreatments of the nonlinear integro-fractional differential equations of theVolterra-Hammerstein type with difference kernel and such a problem which thekernel has a first order simple degenerate kind which the higher-multi fractionalderivative is described in the Caputo sense. In these methods, the solution of afunctional equation is considered as the sum of infinite series of components afterapplying the inverse of Laplace transformation usually converging to the solution,where a closed form solution is not obtainable, a truncated number of terms isusually used for numerical purposes. Finally, examples are prepared to illustratethese considerations.