A Modified Iterative Approach for Solving Linear Fractional-Order Delay Differential Equations
Article Sidebar
Page Numbers:
1581-1592
Digital Object Identifier:
10.58578/yasin.v5i2.5363
Viewed: 298 times
Downloaded: 141 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, Michael Cornelius4, U. M. Nasir5, Okai J. O6*
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) for solving linear fractional-order delay differential equations (FDDEs). The method is assessed through illustrative example, showcasing its effectiveness in producing accurate approximations for linear case, particularly when the fractional order approaches an integer. MNIM demonstrates strong performance in solving equations of integer and near-integer fractional order. However, the accuracy declines as the fractional order moves further from an integer, especially over larger intervals. MNIM remains a powerful and adaptable method for handling a broad spectrum of fractional differential equations involving delays.
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
-
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
-
Boyjanov N.I. (2027)Mathematical analysis of the linear increase in SiO2 content during the activation of Navbakhor alkaline bentonite with hydrochloric acidKompleksnoe Ispolzovanie Mineralnogo Syra, 342(3), 90-99
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