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

  • Shazad Sh. Ahmed Department of Mathematics, College of Science, Sulaimani University, Sulaimanyah, Kurdistan Region, Iraq
  • Shokhan Ahmed Hama Salih Department of Mathematics, College of Science, Sulaimani University, Sulaimanyah, Kurdistan Region, Iraq
  • Mariwan R. Ahmed Department of Science, College of Basic Education, Charmo University, Chamchamal, Kurdistan Region, Iraq
Keywords: Integro-Fractional Differential Equation, Caputo-fractional derivative, Adomian decomposition method, Modified Adomian decomposition method, Noise term phenomenon, Laplace transform

Abstract

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

Published
2019-10-28
How to Cite
Ahmed, S. S., Salih, S. A. H., & Ahmed, M. R. (2019). Laplace Adomian and Laplace Modified Adomian Decomposition Methods for Solving Nonlinear Integro-Fractional Differential Equations of the Volterra-Hammerstein Type. Iraqi Journal of Science, 60(10), 2207-2222. https://doi.org/10.24996/ijs.2019.60.10.15
Section
Mathematics