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.
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PY - 2022/8/11
Y1 - 2022/8/11
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
SN - 2075-1680
VL - 11
SP - 398
JO - Axioms
JF - Axioms
IS - 8
M1 - 8
ER -