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Open Access ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

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Open Access Research Article

Analytical solutions for solving Riccati differential equation with fractional using Elzaki transform decomposition method

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pp. 831–836Vol. 28Issue 3-AApril 2025DOI: 10.47974/JIM-1980XML
Received:
08 May 2024
Published Online:
08 May 2025
Article type:
Research Article
Language:
EN
Article no.:
JIM-1980
Pages:
831–836

Abstract

The Elzaki Adomian Decomposition Method (ETADM), an efficient and powerful technique, is used to analyze several nonlinear fractional Riccati differential equations. This method, which employs Elzaki transformation and an iterative approach, outperforms other techniques by not requiring additional computations or resources. It also eliminates the need for discretization or restrictive assumptions, making it a straightforward and efficient solution. Our study demonstrates that this method is reliable, efficient, and a simple way to address specific issues in various engineering and applied scientific domains.

Keywords

Subject Classifications

35R6035R1132W50

References

[1] I. Podlubny, Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications. Amsterdam, The Netherlands: Elsevier (1998).
[2] R. Metzler and J. Klafter, “The random walk’s guide to anomalous diffusion: A fractional dynamics approach,” Physics Reports, vol. 339, pp. 1–77, Dec. (2000).
[3] D. Baleanu and J. H. Kamil, “A novel approach for Korteweg-de Vries equation of fractional order,” Journal of Applied and Computational Mechanics, vol. 5, no. 2, pp. 192–198 (2019).
[4] H. K. Jassim, “The approximate solutions of three-dimensional diffusion and wave equations within local fractional derivative operator,” in Abstract and Applied Analysis. London, U.K.: Hindawi (2016).
[5] H. K. Jassim, “Homotopy perturbation algorithm using Laplace transform for Newell-Whitehead-Segel equation,” International Journal of Advanced and Applied Mathematics and Mechanics, vol. 2, no. 4, pp. 8–12 (2015).
[6] F. S. Fadhel and H. O. Altaie, “Solution of Riccati matrix differential equation using new approach of variational iteration method,” International Journal of Nonlinear Analysis and Applications, vol. 12, no. 2, pp. 1633–1640 (2021).
[7] A. Atangana and D. Baleanu, “Nonlinear fractional Jaulent-Miodek and Whitham-Broer-Kaup equations within Sumudu transform,” Abstract and Applied Analysis (2013).
[8] M. G. Mousa and H. O. Altaie, “Study on approximate analytical methods for nonlinear differential equations,” Journal of Interdisciplinary Mathematics, vol. 25, no. 8, pp. 2623–2629 (2022).
[9] S. Javeed, D. Baleanu, A. Waheed, M. S. Khan, and H. Affan, “Analysis of homotopy perturbation method for solving fractional order differential equations,” Mathematics, vol. 7, p. 40 (2019).
[10] H. M. Ali, “An efficient approximate-analytical method to solve time-fractional KdV and KdVB equations,” Information Sciences Letters, vol. 9, pp. 189–198 (2020).
[11] S. S. Ray and R. K. Bera, “An approximate solution of a nonlinear fractional differential equation by Adomian decomposition method,” Applied Mathematics and Computation, vol. 167 (2005).
[12] H. O. Altaie, “Two efficient methods for solving nonlinear fourth-order PDEs,” International Journal of Nonlinear Analysis and Applications, vol. 11, pp. 543–546 (2020).
[13] F. Evirgen, “Analyze the optimal solutions of optimization problems by means of fractional gradient-based system using VIM,” International Journal of Optimization, Control, Theories and Applications, vol. 6, pp. 75–83 (2016).
[14] S. Sharma and A. J. Obaid, “Mathematical modelling, analysis and design of fuzzy logic controller for the control of ventilation systems using MATLAB fuzzy logic toolbox,” Journal of Interdisciplinary Mathematics, vol. 23, no. 4, pp. 843–849 (2020).

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