TARU PUBLICATIONS
Journal of Interdisciplinary Mathematics cover
Hybrid ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

Monthly Journal: Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Open Access Research Article

Modified adomian decomposition method for solving PDEs of fractional order

* , ,

* Corresponding author · click or hover a name for details

pp. 1137–1143Vol. 28Issue 3-BApril 2025DOI: 10.47974/JIM-2115XML
Received:
08 Oct 2024
Published Online:
08 May 2025
Article type:
Research Article
Language:
EN
Article no.:
JIM-2115
Pages:
1137–1143

Abstract

A modify approach for approximating an analytical solution of some PDEs with fractional order is the Variational Adomian decomposition methodology (VIADM). We provide several examples to support our conclusions. the results of the solutions process showed that the suggested approach is highly simple, dependable, and effective. The outcomes demonstrate the effectiveness and accuracy of current technology in solving a variety of applied scientific nonlinear challenges. All of the calculations and visualizations were done using the MATLAB R2024B software. In Caputo Sense, fractional derivatives are mentioned. Additionally, a graphical representation of the solutions to a few cases was created. Solution graphs are displayed for problems of both integer and fractional order.

Keywords

Subject Classifications

35R1135R60

References

[1] R. Abazari and M. Abazari, “Numerical simulation of generalized Hirota–Satsuma coupled KdV equation by RD𝓉M and comparison with DTM,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 2, pp. 619–629 (2012).
[2] H. Altaie, “Performance of two-way nesting techniques for shallow water models,” International Journal of Mechanical Engineering and Technology, vol. 7, no. 6, pp. 425–434 (2016).
[3] G. Adomian and R. Rach, “Modified Adomian polynomials,” Mathematical and Computer Modeling, vol. 24, pp. 39–46 (1996).
[4] M. Al-Mazmumy, A. Al-Mutairi, and K. Al-Zahrani, “An efficient decomposition method for solving Bratu’s boundary value problem,” American Journal of Computational Mathematics, vol. 7, no. 1, pp. 84–93 (2017).
[5] A. M. Mohammed and H. O. Altaie, “Analytical solutions via coupled Elzaki Adomian decomposition method for some applications,” Journal of Interdisciplinary Mathematics, vol. 27, no. 4, pp. 761–766 (2024).
[6] A. M. Wazwaz, “Adomian decomposition method for a reliable treatment of the Emden–Fowler equation,” Applied Mathematics and Computation, vol. 161, pp. 543–560 (2005).
[7] M. D. Aloko, O. J. Fenuga, and S. A. Okunuga, “Modified variational iteration method for the numerical solutions of some non-linear Fredholm integro-differential equations of the second kind,” Journal of Applied Computational Mathematics, vol. 6, no. 4, p. 1 (2017).
[8] L. Ebiwareme, “Application of semi-analytical iteration techniques for the numerical solution of linear and nonlinear differential equations,” International Journal of Mathematics Trends and Technology (IJMTT), vol. 67 (2021).
[9] J. H. He, “Variational iteration method for autonomous ordinary differential systems,” Applied Mathematics and Computation, vol. 114, no. 2–3, pp. 115–123 (2000).
[10] O. A. Salman and H. O. Altaie, “Analytical approximate solutions of random integro-differential equations with Laplace decomposition method,” Journal of Interdisciplinary Mathematics, vol. 27, no. 4, pp. 907–912 (2024).
[11] M. A. Z. Raja and S. U. I. Ahmad, “Numerical treatment for solving one-dimensional Bratu problem using neural networks,” Neural Computing and Applications, vol. 24, no. 3–4, pp. 549–561 (2014).
[12] A. M. Mohammed and H. O. Altaie, “Elzaki transform decomposition approach to solve Riccati matrix differential equations,” Journal of Interdisciplinary Mathematics, vol. 27, no. 4, pp. 767–773 (2024).
[13] H. Ahmad (Trans.), “Variational iteration approach for solving fractional integro-differential equations with conformable differintegrals,” Babylonian Journal of Mathematics, pp. 45–49 (2023). doi: 10.58496/BJM/2023/009.
[14] M. M. Abbood, H. H. Ebrahim, A. Al-Fayadh, and A. J. Obaid, “Measure defined on Γ-algebra and some of their generalizations,” Journal of Interdisciplinary Mathematics, vol. 26, no. 5, pp. 821–827 (2023). doi: 10.47974/JIM-1502.

Views: 182Downloads: 86Citations: 0