A survey of (2+1)-dimensional KdV–mKdV equation using nonlocal Caputo fractal–fractional operator

Abdul Jamal, Aman Ullah, Shabir Ahmad, Shahzad Sarwar, Ali Shokri*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We analyze the nonlinear (2+1)-dimensional KdV–mKdV equation with Caputo fractal–fractional operator. Some theoretical features are demonstrated via fixed point results. The solution of the considered KdV–mKdV is studied by the composition of the J-transformation and decomposition method. For the validity and effectiveness of the considered method, two examples with suitable initial conditions are solved, where best agreements observed. The validity of the suggested approach is verified by convergence analysis and Picard stability. From the simulations of the obtained results, it is noted that fractional order and fractal dimension significantly affects the amplitude and shape of wave solutions.

Original languageEnglish
Article number106294
JournalResults in Physics
StatePublished - Mar 2023

Bibliographical note

Funding Information:
All authors approved the version of the manuscript to be published.

Publisher Copyright:
© 2023 The Author(s)


  • Caputo operator
  • J-transform
  • KdV equation
  • Kink soliton

ASJC Scopus subject areas

  • Physics and Astronomy (all)


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