Discontinuity, Nonlinearity, and Complexity 14(4) (2025) 687--706 | DOI:10.5890/DNC.2025.12.006

Maha M. Hamood$^{1,2}$, Abdulrahman A. Sharif$^{2,3}$, Kirtiwant P. Ghadle$^2$

$^{1}$ Department of Mathematics, Taiz University, Taiz-Yemen

$^{2} $ Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, India

$^{3}$ Department of Mathematics, Hodeidah University, AL-Hudaydah-Yemen

Abstract

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.

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