A Modified New Iterative Method for Solving Nonlinear Fractional-Order Delay Differential Equations
Article Sidebar
Page Numbers:
419-438
Digital Object Identifier:
10.58578/ijemt.v3i2.5381
Viewed: 221 times
Downloaded: 214 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:Ibrahim M. D1*, M. M. Adamu2, I. B. Mshelia3, A. M. Kwami4, Okai J. O5, Nyikyaa M. N6
Copyright :Authors retain copyright and grant the journal right of first publication.
Main Article Content
Abstract
This paper explores the application of the Modified New Iterative Method (MNIM) to solve nonlinear fractional-order delay differential equations (NFDDEs). A series of test problems are presented to evaluate the method's performance across various fractional orders. The results indicate that MNIM yields highly accurate approximations, particularly when the fractional order approaches an integer. The method is especially effective for integer-order cases and for fractional orders close to them. However, its accuracy decreases as the fractional order becomes smaller, with noticeable errors emerging over larger domains. MNIM remains a powerful and adaptable approach for solving a broad class of fractional differential equations.
Downloads
Citation Metrics & Similar Scopus Articles
-
Lukpanov R.E. (2027)Evaluation of the Effect of Additives on the Workability of Concrete Mix as Part of a Study of a Modified Wall BlockKompleksnoe Ispolzovanie Mineralnogo Syra, 342(3), 100-110
-
Sadati Nooshabadi S.M. (2027)Object Agreement: A Syntactic Phenomenon in Middle Persian Zoroastrian TextsLanguage Related Research, 17(4), 71-101
-
Rezaei R. (2027)A Analyzing feminine images of language in “Autumn is the Last Season of the Year” by Nasim Marashi, based on Sarah Mills’ patternLanguage Related Research, 17(4), 361-395
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
Ashitha, P. A., & Ranjini, M. C. (2020). On the numerical solution of fractional Riccati differential equations. Malaya Journal of Matematik, 5(1), 214–219.
Daftardar-gejji, V., & Bhalekar, S. (2010). Solving fractional boundary value problems with Dirichlet boundary conditions using a new iterative method. Computers and Mathematics with Applications, 59(5), 1801–1809. https://doi.org/10.1016/j.camwa.2009.08.018
Daftardar-gejji, V., & Jafari, H. (2006). An iterative method for solving nonlinear functional equations. J. Math. Anal. Appl., 316(2006), 753–763. https://doi.org/10.1016/j.jmaa.2005.05.009
Du, M. J. (2022). A Specific Method for Solving Fractional Delay Differential Equation via Fraction Taylor’s Series. Mathematical Problems in Engineering, 2022, 1–6. https://doi.org/10.1155/2022/4044039
El-Kalla, I. L., Elgaber, K. M. A., Elmahdy, A. R., & Sayed, A. Y. (2019). Solution of a Nonlinear Delay Differential Equation Using Adomian Decomposition Method with Accelerated Formula of Adomian Polynomial. American Journal of Computational Mathematics, 09(04), 221–233. https://doi.org/10.4236/ajcm.2019.94017
Goswami, P., & Alqahtani, R. T. (2016). Solutions of fractional differential equations by Sumudu transform and variational iteration method. Journal of Nonlinear Science and Applications, 9(4), 1944–1951. https://doi.org/10.22436/jnsa.009.04.48
Mohyud-din, S. T., & Yildirim, A. (2010). Variational Iteration Method for Delay Differential Equations Using He ’ s Polynomials. HITEC U, 1(2), 1045–1048.
Moltot, A. T., & Deresse, A. T. (2022). Approximate Analytical Solution to Nonlinear Delay Differential Equations by Using Sumudu Iterative Method. Advances in Mathematical Physics, 2022(2), 1–18. https://doi.org/10.1155/2022/2466367
Ramadan, M. A. (2015). New iterative method for cauchy problems. J. Math.Comput.Sci., 5(6), 826–835.
Saeed, R. K., & Rahman, B. M. (2011). Differential Transform Method for Solving System of Delay Differential Equation. Australian Journal of Basic and Applied Sciences, 5(4), 201–206.
Srivastava, V. (2020). Approximate Analytical Solution of Linear and Nonlinear Fractional Delay Differential Equations using Variational Iteration Method Abstract : Open Science Journal, 5(4), 1–11.
Vilu, S., Ahmad, R. R., & Din, U. K. S. (2019). Variational Iteration Method and Sumudu Transform for Solving Delay Differential Equation. International Journal of Differential Equations, 2019(1), 1–6. https://doi.org/10.1155/2019/6306120