Hybrid of Semi-Analytical Methods for the Solution of Fractional Fredholm Integro-Differential Equations

M.Z. Olakanse¹ , J.O. Okai² , Micheal Cornelius³

Section:Research Paper, Product Type: Journal-Paper
Vol.11 , Issue.6 , pp.39-46, Dec-2024

Online published on Dec 31, 2024

Copyright © M.Z. Olakanse, J.O. Okai, Micheal Cornelius . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
This seminar introduces a hybrid approach combining the Adomian Decomposition Method (ADM) and the Variational Iteration Method (VIM) to enhance the performance of ADM (Ansari & Ahmad, 2023) in solving fractional integro-differential equations. The primary objective of the research is to eliminate the use of Lagrange’s multiplier in ADM and the Adomian polynomial in VIM. A new scheme is proposed, offering series solutions for both integer and non-integer orders. The proposed method demonstrates superiority over its counterparts, and several examples are presented to validate its effectiveness.

Key-Words / Index Term :
Fractional integro-differential equation, Adomian decomposition method, Variational Iteration method

References :
[1] I. Podlubny, Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications. Academic Press, 1999.
[2] Y. Song, "Numerical solutions of fractional differential equations using modified variational iteration method," Mathematical Problems in Engineering, vol. 2016, pp. 1–12, 2016.
[3] M. A. F. Araghi, S. G. Dogaheh, and Z. Sayadi, "The modified variational iteration method for solving linear and nonlinear ordinary differential equations," Australian Journal of Basic and Applied Sciences, vol. 5, no. 10, pp. 406–416, 2011.
[4] T. A. Abassy, "Modified variational iteration method (non-homogeneous initial value problem)," Mathematical and Computer Modelling, vol. 55, no. 3–4, pp. 1222–1232, 2012.
[5] A. Ansari and N. Ahmad, "Numerical accuracy of Fredholm linear integro-differential equations by using Adomian decomposition method, modified Adomian decomposition method, and variational iteration method," Journal of Science and Arts, vol. 23, no. 3, pp. 625–638, 2023.
[6] A. M. Wazwaz, A First Course in Integral Equations. World Scientific Publishing Company, 2007.
[7] T. Oyedepo, C. Yemisi, A. Ajimoti, and O. Lukman, "Computational algorithm for fractional Fredholm integro-differential equations," Kathmandu University Journal of Science, Engineering and Technology, vol. 17, no. 1, pp. 1–6, 2023.
[8] K. Diethelm, The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type. Springer, 2010.
[9] A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations. Elsevier, 2006