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A Possible Generalization of Acoustic Wave Equation Using the Concept of Perturbed Derivative Order

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  • Abdon Atangana
  • Adem Kılıçman

Abstract

The standard version of acoustic wave equation is modified using the concept of the generalized Riemann-Liouville fractional order derivative. Some properties of the generalized Riemann-Liouville fractional derivative approximation are presented. Some theorems are generalized. The modified equation is approximately solved by using the variational iteration method and the Green function technique. The numerical simulation of solution of the modified equation gives a better prediction than the standard one.

Suggested Citation

  • Abdon Atangana & Adem Kılıçman, 2013. "A Possible Generalization of Acoustic Wave Equation Using the Concept of Perturbed Derivative Order," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-6, April.
    • Handle: RePEc:hin:jnlmpe:696597
    DOI: 10.1155/2013/696597
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    Cited by:

    1. Panda, Sumati Kumari & Ravichandran, C. & Hazarika, Bipan, 2021. "Results on system of Atangana–Baleanu fractional order Willis aneurysm and nonlinear singularly perturbed boundary value problems," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. Tahereh Eftekhari & Jalil Rashidinia, 2023. "An Investigation on Existence, Uniqueness, and Approximate Solutions for Two-Dimensional Nonlinear Fractional Integro-Differential Equations," Mathematics, MDPI, vol. 11(4), pages 1-29, February.

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