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Construction of Solitons and Other Wave Solutions for Generalized Kudryashov’s Equation with Truncated M-Fractional Derivative Using Two Analytical Approaches

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Abstract

In the current work, the modified simplest equation approach and modified \((G'/G^2)\)-expansion approach are implemented to extract soliton solutions and other exact solutions for generalized Kudryashov’s equation with truncated M-fractional derivative. Various types of solutions are extracted such as dark soliton solutions, bright-singular soliton solutions, singular soliton solutions, combo singular solitons solutions, combo dark-singular soliton solutions, periodic solutions and rational solutions. Moreover, to emphasise the impact of truncated M-fractional derivative on the behaviour solutions for the presented problem, the 2D, 3D and contour representations of some obtained solutions are produced. The introduced methods are more reliable, applicability and simple as compared to many other methods to solve the nonlinear fractional partial differential equations.

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Author information

Authors and Affiliations

  1. Math Center, House No 87 Rahmanyia Colony, Vehari, Pakistan

    Waseem Razzaq

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

    Asim Zafar

  3. Department of Physics and Engineering Mathematics, Higher Institute of Engineering, El Shorouk Academy, El-Shorouk City, Cairo, Egypt

    Hamdy M. Ahmed

  4. Department of Physics and Engineering Mathematics, Higher Institute of Engineering and Technology, Tanta, Egypt

    Wafaa B. Rabie

Authors
  1. Waseem Razzaq
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  2. Asim Zafar
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  3. Hamdy M. Ahmed
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  4. Wafaa B. Rabie
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Contributions

WR: Writing—reviewing, methodology, validation, software. AZ: supervision, writing. HMA: reviewing and editing. WBR: software, writing—reviewing and editing.

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Correspondence to Hamdy M. Ahmed.

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Razzaq, W., Zafar, A., Ahmed, H.M. et al. Construction of Solitons and Other Wave Solutions for Generalized Kudryashov’s Equation with Truncated M-Fractional Derivative Using Two Analytical Approaches. Int. J. Appl. Comput. Math 10, 21 (2024). https://doi.org/10.1007/s40819-023-01660-x

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