Solving a Generalized Fractional Nonlinear Integro-Differential Equations via Modified Sumudu Decomposition Transform

Kamel Al-Khaled*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The Sumudu decomposition method was used and developed in this paper to find approximate solutions for a general form of fractional integro-differential equation of Volterra and Fredholm types. The Caputo definition was used to deal with fractional derivatives. As the method under consideration depends mainly on writing non-linear terms, which are often found inside the kernel of the integral equation, writing it in the form of Adomian’s polynomials in the well-known way. After applying the Sumudu transformation to both sides of the integral equation, the solution was written in the form of a convergent infinite series whose terms can be alternately calculated. The method was applied to three examples of non-linear integral equations with fractional derivatives. The results that were presented in the form of tables and graphs showed that the method is accurate, effective and highly efficient.

Original languageEnglish
Article number398
JournalAxioms
Volume11
Issue number8
DOIs
Publication statusPublished - Aug 2022
Externally publishedYes

Keywords

  • adomian decomposition
  • approximate solutions
  • fractional integro-differential equation
  • sumudu transform

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Mathematical Physics
  • Logic
  • Geometry and Topology

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