A Hybrid Approach of the Variational Iteration Method and Adomian Decomposition Method for Solving Fractional Integro-Differential Equations
Article Sidebar
Page Numbers:
2681-2706
Digital Object Identifier:
10.58578/yasin.v5i4.5720
Viewed: 354 times
Downloaded: 130 times
LYAS Publisher cordially invites qualified professionals to serve as Editors or Reviewers. Your expertise will make an important contribution to maintaining and strengthening the academic quality of our publications. Interested applicants are kindly requested to complete the application form at the following link: Editors & Reviewers
Please feel free to contact us if you need any further information about the submission process or if you have any additional questions.
Authors:Okai J. O1*, M. S. Adamu2, Cornelius M.3, Abdulmalik I.4, Jeremiah A.5, Nasir U. M.6, Hafsat Y. U.7, Abichele O.8, Hassan Araga9
Copyright :Authors retain copyright and grant the journal right of first publication.
Main Article Content
Abstract
In this study, we propose a hybrid analytical technique that integrates the Adomian Decomposition Method (ADM) with the Variational Iteration Method (VIM) to solve both linear and nonlinear integro-differential equations of integer and fractional orders. This approach extends and refines the Odibat Decomposition Method (ODM) by addressing key limitations inherent in ADM and VIM—specifically, the reliance on linearization, Adomian polynomials, and Lagrange multipliers. By circumventing these computational complexities, the proposed method enables the direct and efficient construction of series solutions with improved convergence properties. The hybrid scheme is designed for broader applicability and enhanced computational simplicity, making it a powerful tool for analyzing complex integro-differential systems. Its effectiveness and robustness are demonstrated through a range of illustrative examples, confirming the method’s capability to provide accurate analytical approximations with minimal computational overhead.
Citation Metrics:
Downloads
Citation Metrics & Similar Scopus Articles
-
Shamuratov S.X. (2027)Sigmoid Neutralization Response of Acidic Soapstock Waste by Mineralized Phosphorite Residues: A 4-Parameter Logistic ApproachKompleksnoe Ispolzovanie Mineralnogo Syra, 342(3), 80-89
-
Sadati Nooshabadi S.M. (2027)Object Agreement: A Syntactic Phenomenon in Middle Persian Zoroastrian TextsLanguage Related Research, 17(4), 71-101
-
Najafi E. (2027)Analyzing the process of dynamic and tense discourse systems in the poem "katibeh" of Akhavan salesLanguage Related Research, 17(4), 263-291
Article Details
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
References
Bhalekar, S., & Daftardar-gejji, V. (2012). Solving Fractional-Order Logistic Equation Using a New Iterative Method. 2012. https://doi.org/10.1155/2012/975829
Hemeda, A. A. (2018). A Friendly Iterative Technique for Solving Nonlinear Integro-Differential and Systems of Nonlinear Integro-Differential Equations. International Journal of Computational Methods, 15(1), 1–15. https://doi.org/10.1142/S0219876218500160
Ilejimi D.O, O. J. . and R. R. . (2019). On The Numerical Solution of Picard Iteration Method for Fractional Integro - Differential Equation. International Journal of Scientific and Research Publications, 9(3), 367–373. https://doi.org/10.29322/IJSRP.9.03.2019.p8757
Rashidi, M.M., Rabiei, F., Naseri Nia S. and Abbasbandy, S. (2020). A Review : Differential Transform Method. Int. J. of Applied Mechanics and Engineering, 25(2), 122–129. https://doi.org/10.2478/ijame-2020-0024
Momani, S., & Odibat, Z. (2007). Homotopy perturbation method for nonlinear partial differential equations of fractional order. Physics Letters, Section A: General, Atomic and Solid State Physics, 365(5–6), 345–350. https://doi.org/10.1016/j.physleta.2007.01.046
Odibat, Z. (2019). An optimized decomposition method for nonlinear ordinary and partial differential equations. Physica A, 123-323.https://doi.org/10.1016/j.physa.2019.123323
Okai, J. (2020). On The Reduced Form Of The Adomian Polynomials For The Solutions Of Nonlinear Fractional-Order Volterra Integro-Differential Equations. International Journal of Scientific and Research Publications, 10(6), 837-847.https://doi.org/10.29322/IJSRP.10.06.2020.p10299
Rawashdeh, E. A. (2006). Numerical solution of fractional integro-differential equations by collocation method. Applied Mathematics and Computation, 176(2006), 1–6. https://doi.org/10.1016/j.amc.2005.09.059
Tate, S., & Dinde, H. T. (2019). A New Modification of Adomian Decomposition Method for Nonlinear Fractional-Order Volterra Integro-Differential Equations. 15(1), 33–41.
Wang, J., Jamal, A., & Li, X. (2021). Numerical Solution of Fractional-Order Fredholm Integrodifferential Equation in the Sense of Atangana – Baleanu Derivative. Hindawi Mathematical Problems in Engineering, 2021(8), 30–32.
Wazwaz, A. M. (2009). The variational iteration method for analytic treatment for linear and nonlinear ODEs. Applied Mathematics and Computation, 212(1), 120–134. https://doi.org/10.1016/j.amc.2009.02.003
Yang, C. (2013). Numerical solution of integro-differential equations of fractional order by Laplace decomposition method. Wseas Transactions On Mathematics, 12(12), 1173–1183.
Ziane, D., & Cherif, M. H. (2018). Variational iteration transform method for fractional differential equations. Journal of Interdisciplinary Mathematics, 21(1), 185–199. https://doi.org/10.1080/09720502.2015.1103001