Innovative Insights and Fractal-View of Phi-Four Equations with Time Fractal Derivative

Authors

  • Rashida Qayyum Khan Department of Mathematics, RIPHAH International University, Faisalabad, Pakistan
  • H. M. Younas Department of Mathematics, RIPHAH International University, Faisalabad, Pakistan
  • Shauket Ali Tahir Department of Mathematics and Statistics, The University of Lahore, Lahore Pakistan

DOI:

https://doi.org/10.52280/5444r715

Keywords:

Homotopy perturbation method, Fractional order calculus, Fractal Phi-four equation with respect to time, Estimated solution, Caputo operator, Riemann-Liouville fractional integral operator

Abstract

 In this work, a new analytical technique recognized as the homotopy perturbation method is utilized to identify the general solutions of Phi-4 nonlinear partial differential equations of fractional order with respect to time. The first order general solution is determined by HPM and then compared with the exact result. It can be seen that the result obtained using HPM shows a large convergence rate for Phi-4 partial differential equations with time fractal derivative. The exact graphic solutions have been shown, and their respective errors have also been represented usingtables.

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Published

2025-01-20

Issue

Vol. 57 No. 9 (2025): PUJM

Section

Articles

License

Copyright (c) 2026 Rashida Qayyum Khan, H. M. Younas, Shauket Ali Tahir

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Innovative Insights and Fractal-View of Phi-Four Equations with Time Fractal Derivative. (2025). Punjab University Journal of Mathematics, 57(9), 915-935. https://doi.org/10.52280/5444r715