- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 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 Abdelkrim, Mouffak Benchohra, Jamal Eddine Lazreg, Johnny Henderson
Pages : 173-190
Doi:10.31197/atnaa.973992
View : 5 | Download : 16
Publication Date : 2022-06-30
Article Type : Research
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