Fractional differential equations with a \(\psi \)-Hilfer fractional derivative

Abstract

In this paper, we consider a fractional differential equations involving a \(\psi \)-Hilfer fractional derivative. First, we give a correspondence between our problem and a Volterra-type integral equation. Next, sufficient conditions are given to ensure existence and uniqueness of solutions. Then, a numerical approximation method is used to approximate the solution of the problem. For an appropriate choice of the kernel \(\psi \), we recover most of all the previous results on fractional differential equations.

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Correspondence to Wael Abdelhedi.

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Communicated by José Tenreiro Machado.

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Abdelhedi, W. Fractional differential equations with a \(\psi \)-Hilfer fractional derivative. Comp. Appl. Math. 40, 53 (2021). https://doi.org/10.1007/s40314-021-01447-0

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Keywords

  • Fractional differential equations
  • Fractional calculus

Mathematics Subject Classification

  • 26A33
  • 34A08