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Applications of the Simplest Equation Procedure to Some Fractional Order Differential Equations in Mathematical Physics

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Abstract

The aim of the paper is to find the exact solutions to the nonlinear partial differential equations of fractional-order. The simplest equation procedure is handled for this purpose. The discussed method is utilized to equations which are space-time generalized reaction duffing model of conformable fractional-order which turns into six equations by giving different values to the parameters and space-time density-dependent diffusion–reaction model of conformable fractional-order. The considered equations are reduced to ordinary differential equations with the help of the wave transformations in the first step. According to the discussed methods form of the exact solutions are given by using the homogeneous balance number in step two. These exact solutions are substituted in the obtained ordinary differential equations without ignoring \(\phi '(\epsilon )=\phi ^2(\epsilon )+\varsigma \) in step three. When the obtained determining equation system is solved, the exact solutions of the given equations are obtained in the last step. The obtained solutions are expressed by rational, trigonometric and hyperbolic solutions. 3D, 2D and contour plots are drawn for some obtained exact solutions.

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Authors and Affiliations

  1. Math Center, Rahmanyia Colony, Vehari, Pakistan

    Waseem Razzaq

  2. Department of Mathematics, CUI, Vehari Campus, Vehari, Pakistan

    Waseem Razzaq & Asim Zafar

  3. Department of Mathematics, Art-Science Faculty, Bursa Uludag University, Bursa, Turkey

    Arzu Akbulut

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  1. Waseem Razzaq
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  2. Asim Zafar
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Razzaq, W., Zafar, A. & Akbulut, A. Applications of the Simplest Equation Procedure to Some Fractional Order Differential Equations in Mathematical Physics. Int. J. Appl. Comput. Math 10, 56 (2024). https://doi.org/10.1007/s40819-024-01687-8

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