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Analytical Solutions of (2+Time Fractional Order) Dimensional Physical Models, Using Modified Decomposition Method
Open AccessArticle

Fractional View Analysis of Acoustic Wave Equations, Using Fractional-Order Differential Equations

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Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan
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Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530 Ankara, Turkey
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Institute of Space Sciences, 077125 Magurele, Romania
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Center of Excellence in Theoretical and Computational Science (TaCS-CoE) & Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand
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Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
*
Author to whom correspondence should be addressed.
Appl. Sci. 2020, 10(2), 610; https://doi.org/10.3390/app10020610
Received: 1 November 2019 / Revised: 13 December 2019 / Accepted: 15 December 2019 / Published: 15 January 2020
In the present research work, a newly developed technique which is known as variational homotopy perturbation transform method is implemented to solve fractional-order acoustic wave equations. The basic idea behind the present research work is to extend the variational homotopy perturbation method to variational homotopy perturbation transform method. The proposed scheme has confirmed, that it is an accurate and straightforward technique to solve fractional-order partial differential equations. The validity of the method is verified with the help of some illustrative examples. The obtained solutions have shown close contact with the exact solutions. Furthermore, the highest degree of accuracy has been achieved by the suggested method. In fact, the present method can be considered as one of the best analytical techniques compared to other analytical techniques to solve non-linear fractional partial differential equations. View Full-Text
Keywords: homotopy perturbation method; variational iteration method; Laplace transform method; acoustic wave equations homotopy perturbation method; variational iteration method; Laplace transform method; acoustic wave equations
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MDPI and ACS Style

Ali, I.; Khan, H.; Shah, R.; Baleanu, D.; Kumam, P.; Arif, M. Fractional View Analysis of Acoustic Wave Equations, Using Fractional-Order Differential Equations. Appl. Sci. 2020, 10, 610.

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