ANALYSIS AND SIMULATION OF FRACTIONAL-ORDER WAVE-LIKE EQUATIONS UNDER CAPUTO FRACTIONAL OPERATOR

Abdul Hamid Ganie

doi:10.11948/20250356

2026 Volume 16 Issue 5

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Abdul Hamid Ganie. ANALYSIS AND SIMULATION OF FRACTIONAL-ORDER WAVE-LIKE EQUATIONS UNDER CAPUTO FRACTIONAL OPERATOR[J]. Journal of Applied Analysis & Computation, 2026, 16(5): 2584-2605. doi: 10.11948/20250356

Citation:

Abdul Hamid Ganie. ANALYSIS AND SIMULATION OF FRACTIONAL-ORDER WAVE-LIKE EQUATIONS UNDER CAPUTO FRACTIONAL OPERATOR[J]. Journal of Applied Analysis & Computation, 2026, 16(5): 2584-2605. doi: 10.11948/20250356

ANALYSIS AND SIMULATION OF FRACTIONAL-ORDER WAVE-LIKE EQUATIONS UNDER CAPUTO FRACTIONAL OPERATOR

Abdul Hamid Ganie^1, ,

1.
Basic Sciences Department, College of Science and Theoretical Studies, Saudi Electronic University, PO Box: 93499, Riyadh 11673, Saudi Arabia

Corresponding author: Email: a.ganie@seu.edu.sa(A. H. Ganie)

Abstract

Abstract

This paper examines the two methods for resolving nonlinear Caputo time-fractional wave-like equations with variable coefficients. These two methods have the names Homotopy perturbation transform method and Elzaki transform decomposition method. I first turn the problem into its differential partner with the use of the Elzaki transform, and then used the He's polynomials as well as adomian polynomials to calculate the nonlinear terms. The simplicity and accuracy of given techniques are illustrated by three different numerical examples. The obtained results indicate the reliability and efficacy of the two methods, both of which give estimations with greater accuracy, precession and closed-form solutions. The mentioned techniques can be utilized to generate the solutions to these types of equations as infinite series, and when these series admit closed form, they offer the precise solution. Numerical and graphical simulations are used to confirm the usefulness of the suggested approaches. It is confirmed that the methods yield solutions converging to the exact solution at an adequate rate. Moreover, we include solution profiles that outline the behavior of the acquired findings, helping researchers grasp the impact of the fractional order. It has been shown that the suggested strategies are efficient and successful when it is implemented. The accuracy and efficacy of the technique are examined using three numerical examples.
- Elzaki transform /
- analytical techniques /
- nonlinear time-fractional wave-like equations /
- Caputo operator
MSC: 35A20, 35L05, 26A33

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References

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