Enhancing the Daftardar Jafari Method for Solving the Bagley–Torvik Equation through Numerical Approaches

Main Article Content

A. A Saje
A. M Kwami
A. G Madaki
Okai J. O
I. M. Waziri
Yakubu Hafsat

Abstract

A robust algorithm is introduced in the development of the Enhanced Daftardar Jafari Method (DJM) to effectively address both linear and nonlinear Bagley–Torvik equations (BTE) and other fractional order differential equations. The method's efficacy is demonstrated through numerical examples, showcasing its ability to solve these equations without resorting to linearization or small perturbations. The results affirm the method's strength, accuracy, and simplicity in comparison to alternative approaches.

Keywords:
Share Article:

Citation Metrics:

Scopus



Downloads

Download data is not yet available.

Scopus Citation Data

Data source Crossref
0
citations
Check Secondary Documents in Scopus
Open this article in Scopus, then check the Secondary documents tab. Use Manual Citation Fallback only for counts you have verified manually.
Open in Scopus
Similar Scopus Articles
Scopus
  1. Asl S.B. (2027)
    Uncertainty estimation in earthquake magnitude determination using high-rate GPS data with Bootstrap method
    Iranian Journal of Geophysics, 20(3), 187-203
  2. Shiryazdi R.S. (2027)
    Assessing performances of pattern informatics method variants: a comparative analysis in Zagros, Iran
    Iranian Journal of Geophysics, 20(3), 65-80
  3. Fazl Kazemi A. (2027)
    Revisiting wintertime budget of local finite-amplitude wave activity in the Northern Hemisphere storm tracks
    Iranian Journal of Geophysics, 20(3), 1-24

Article Details

How to Cite
Saje, A. A., Kwami, A. M., Madaki, A. G., O, O. J., Waziri, I. M., & Hafsat, Y. (2025). Enhancing the Daftardar Jafari Method for Solving the Bagley–Torvik Equation through Numerical Approaches. Journal of Multidisciplinary Science: MIKAILALSYS, 3(2), 611-624. https://doi.org/10.58578/mikailalsys.v3i2.5337

References

Abu Arqub, O., & Maayah, B. (2018). Solutions of Bagley–Torvik and Painlevé equations of fractional order using iterative reproducing kernel algorithm with error estimates. Neural Computing and Applications, 29(5), 1465–1479. https://doi.org/10.1007/s00521-016-2484-4

Ashitha, P. A., & Ranjini, M. C. (2020). On the numerical solution of fractional Riccati differential equations. Malaya Journal of Matematik, 5(1), 214–219.

Asif, M., Raja, Z., Khan, J. A., & Qureshi, I. M. (2011). Solution of Fractional Order System of Bagley-Torvik Equation Using Evolutionary Computational Intelligence. Mathematical Problems in Engineering, 1(10), 1–18. https://doi.org/10.1155/2011/675075

Askari, M. (2023). Numerical solution of fractional Bagley – Torvik equations using Lucas. Iranian Journal of Numerical Analysis and Optimization, 13(4), 695–710.

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

Hemeda, A. A. (2015). An integral iterative method for solving fractional physical differential equations. Abstract and Applied Analysis, 18(2), 365–381.

Jianhua Hou, C. Y. and X. L. (2016). Jacobi Collocation Methods for Solving the Fractional Bagley-Torvik Equation. IJAM.Pe, 110(2), 265–273. https://doi.org/10.12732/ijpam.v110i2.3

Mahdy, A. M.; Mukhtar, N. A. (1976). An iterative method for solving nonlinear partial differential equations. Advances in Mathematics, 19(2), 245–265. https://doi.org/10.1016/0001-8708(76)90064-5

Ramadan;Al-luhaibi. (2014). New Iterative Method for Solving the Fornberg-Whitham Equation and Comparison with Homotopy Perturbation Transform Method. British Journal of Mathematics & Computer Science, 4(9), 1213–1227. https://doi.org/10.9734/bjmcs/2014/8534

Ramadan, M. A. (2015). New iterative method for cauchy problems. J. Math.Comput.Sci., 5(6), 826–835.

Torvik, P. J., & Bagley, R. L. (1984). On the Appearance of the Fractional Derivative in the Behavior of Real Materials i : Journal of Applied Mechanics, 51(2), 294–298.


Explore Our Journals
Find the most suitable journal for your research. If this journal does not fully align with the scope of your manuscript, we invite you to explore our wider portfolio of journals covering diverse fields of study. Please select one of the journals below to identify the most appropriate publication platform for your work.

Most read articles by the same author(s)