A note on a class of Caputo fractional differential equations with respect to another function

M. A. Zaky, A. S. Hendy, D. Suragan

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

The mathematical analysis and solutions for a class of ψ-Caputo fractional differential equations are discussed. Assuming that ψ(t) is strictly monotone and armed by the possibility of converting the ψ-Caputo fractional differential equations with respect to another function ψ to its Caputo counterpart by a mapping transformation, the solutions of the ψ-Caputo fractional differential equations can be deduced from the solution representation for the Caputo version via an inverse transformation. We show that the mapping transformation for such derivatives is extremely useful in practical applications. The representation of solutions for constant order time ψ-Caputo fractional diffusion equation and variable order ψ-Caputo fractional mobile-immobile diffusion equation is investigated and the regularity estimates are deduced accordingly.

Original languageEnglish
Pages (from-to)289-295
Number of pages7
JournalMathematics and Computers in Simulation
Volume196
DOIs
Publication statusPublished - Jun 2022

Keywords

  • Analytical solution
  • Existence and uniqueness
  • Fractional derivative with respect to another function
  • Variable-order derivative
  • Well-posedness

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)
  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics

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