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

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Advances in the Theory of Nonlinear Analysis and its Application
Volume:6 Issue:2
On $k$-Generalized $\psi$-Hilfer Boundary Value Problems with Retardation and Anticipation

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

Authors : Salim ABDELKRİM, Mouﬀak BENCHOHRA, Jamal Eddine LAZREG, Johnny HENDERSON

Pages : 173-190

Doi:10.31197/atnaa.973992

View : 11 | Download : 14

Publication Date : 2022-06-30

Article Type : Research Paper

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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