An Investigation of the Bifurcation of Traveling Wave Solutions in Time-Fractional Nonlinear Differential Equations of the Symmetric Case

Authors

  • Mustafa T. Yaseen Department of Management and Marketing for Oil & Gas, College of Industrial Management, Basra University for Oil & Gas, Basrah, Iraq https://orcid.org/0000-0001-7084-8478
  • Mudhir A. Abdul Hussain Department of Mathematics, Education College for Pure Sciences, University of Basrah, Basrah, Iraq https://orcid.org/0000-0002-4730-6942

DOI:

https://doi.org/10.26713/cma.v16i2.2906

Keywords:

Differential equations, Bifurcation analysis, Complex transform

Abstract

This study considers examining and bifurcation of traveling wave solutions in time-fractional nonlinear differential equations of the symmetric case. We blend Li and He’s derivative of fractional order techniques with Lyapunov-Schmidt reduction in our approach. To simplify the analysis, the initial fractional equation that is differential is transformed into a partial differential equation through the utilization of the fractional complex transform. This conversion results in a condensed equation, presented as a pair of nonlinear algebraic equations, tackling the core issue. Furthermore, our investigation involves examining linear approximation solutions for a nonlinear fractional equation (NFE) that is differential.

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Published

20-08-2025
CITATION

How to Cite

Yaseen, M. T., & Hussain, M. A. A. (2025). An Investigation of the Bifurcation of Traveling Wave Solutions in Time-Fractional Nonlinear Differential Equations of the Symmetric Case. Communications in Mathematics and Applications, 16(2), 669–677. https://doi.org/10.26713/cma.v16i2.2906

Issue

Vol. 16 No. 2 (2025)

Section

Research Article

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