On $k$-Generalized $\psi$-Hilfer Boundary Value Problems with Retardation and Anticipation

Year 2022, Volume: 6 Issue: 2, 173 - 190, 30.06.2022

Salim Abdelkrim , Mouffak Benchohra , Jamal Eddine Lazreg , Johnny Henderson

https://doi.org/10.31197/atnaa.973992

Cited By: 11

Abstract

In this paper, we prove some existence and uniqueness results for a class of boundary valued problems for implicit nonlinear
$k$-generalized $\psi$-Hilfer fractional differential equations involving both retarded and advanced arguments. Further, examples are given to illustrate the viability of our results.

Keywords

$\psi$-Hilfer fractional derivative, $k$-generalized $\psi$-Hilfer fractional derivative, Cauchy-type problem, retarded arguments, advanced arguments, existence, uniqueness

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