TY - JOUR

T1 - Solving a Generalized Fractional Nonlinear Integro-Differential Equations via Modified Sumudu Decomposition Transform

AU - Al-Khaled, Kamel

N1 - Funding Information:
This work was supported by Deanship of Research at Jordan University of Science and Technology via grant number 20220348.
Publisher Copyright:
© 2022 by the author.

PY - 2022/8

Y1 - 2022/8

N2 - 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.

AB - 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.

KW - adomian decomposition

KW - approximate solutions

KW - fractional integro-differential equation

KW - sumudu transform

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U2 - 10.3390/axioms11080398

DO - 10.3390/axioms11080398

M3 - Article

AN - SCOPUS:85137342155

VL - 11

JO - Axioms

JF - Axioms

SN - 2075-1680

IS - 8

M1 - 398

ER -