Modeling and Analysis of Dynamic Waveforms in Nonlinear Fractional Models of Fifth Order

Articles in Press

Document Type : Research Paper

Authors

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

2 School of Mathematics, Sichuan University, Chengdu 610065, China.

3 Department of Mathematics, Jagannath University, Dhaka-1100, Bangladesh.

4 Department of Mathematics, Pabna University of Science and Technology, Pabna-6600, Bangladesh.

5 Faculty of Engineering and Technology (FET), Multimedia University, Melaka-75450, Malaysia.

Abstract

The overarching purpose of this work is to derive new exact traveling wave solutions for a fifth-order generalized nonlinear fractional differential
equation (5th-order GNFDE) by applying the Improved Auxiliary equation method. This equation is characterized by M-fractional derivatives (M-FD), which offer a larger basis for modeling complex dynamical systems with memory effects. The proposed methodology enables various types of solutions designed in the shape of traveling wave solutions, solitary wave solutions, and other prominent solution types, indicating the robustness and versatility of the approach in dealing with nonlinear fractional differential equations. Some investigated solutions are demonstrated in 2D and 3D graphics by smearing definite values to the parameters under constrained conditions to boost the key propagating features. The results contribute significantly to the development of analytical techniques for solving high-order nonlinear fractional differential equations (NLFDE). In addition, the method is efficient and applicable to various non-linear systems, further enhancing its practical efficacy.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 29 October 2025

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History

  • Receive Date: 07 July 2025
  • Revise Date: 07 September 2025
  • Accept Date: 06 October 2025

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