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On Generalized Proportional Fractional Order Derivatives and Darboux Problem for Partial Differential Equations

Author

Listed:
  • Abdellatif Ben Makhlouf
  • Mondher Benjemaa
  • Djalal Boucenna
  • Lassaad Mchiri
  • Mohamed Rhaima
  • Rodica Luca

Abstract

The study of the existence and uniqueness of solutions to 2D systems utilizing the generalized proportional fractional derivative operator is the focus of this work. We also derive a finite difference scheme in order to numerically approximate such an operator, and we prove that the method we propose is convergent. Several tests are performed at the end to illustrate the robustness of our algorithm.

Suggested Citation

  • Abdellatif Ben Makhlouf & Mondher Benjemaa & Djalal Boucenna & Lassaad Mchiri & Mohamed Rhaima & Rodica Luca, 2023. "On Generalized Proportional Fractional Order Derivatives and Darboux Problem for Partial Differential Equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2023, pages 1-22, August.
    • Handle: RePEc:hin:jnddns:6648524
    DOI: 10.1155/2023/6648524
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