Study of traveling soliton and fronts phenomena in fractional Kolmogorov-Petrovskii-Piskunov equation

Ikram Ullah, Kamal Shah*, Thabet Abdeljawad

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


The present research work presents the modified Extended Direct Algebraic Method (m-EDAM) to construct and analyze propagating soliton solutions for fractional Kolmogorov-Petrovskii-Piskunov equation (FKPPE) which incorporates Caputo’s fractional derivatives. The FKPPE has significance in various disciplines such as population growth, reaction-diffusion mechanisms, and mathematical biology. By leveraging the series form solution, the proposed m-EDAM determines plethora of travelling soliton solutions through the transformation of FKPPE into Nonlinear Ordinary Differential equation (NODE). These soliton solutions shed light on propagation processes in the framework of the FKPPE model. Our study also offers some graphical representations that facilitate the characterization and investigation of propagation processes of the obtained soliton solutions which include kink, shock soliton solutions. Our work advances our understanding of complicated phenomena across multiple academic disciplines by fusing insights from mathematical biology and reaction-diffusion mechanisms.

Original languageEnglish
Article number055259
JournalPhysica Scripta
Issue number5
Publication statusPublished - 1 May 2024
Externally publishedYes


  • Caputo derivative
  • modified extended direct algebraic approach
  • modified extended direct algebraic approach; Caputo derivative; wave transformation; solitons solutions
  • solitons solutions
  • wave transformation


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