On k -Generalized ψ -Hilfer Boundary Value Problems with Retardation and Anticipation

Open Access

Original research article

Author(s):

Abdelkrim Salim^a, Mouffak Benchohra^a, Jamal Eddine Lazreg^a, Johnny Henderson^b

^a Department of Mathematics, Djillali Liabes University, Sidi Bel-Abbes, Algeria.
^b Department of Mathematics, Baylor University, Waco, Texas, USA.

Advances in the Theory of Nonlinear Analysis and its Applications 6(2), 173–190.

Received: July 24, 2021

Accepted: January 14, 2022

Published: January 17, 2022

Abstract

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

Keywords: ψ-Hilfer fractional derivative, k-generalized ψ-Hilfer fractional derivative, Cauchy-type problem, retarded arguments, advanced arguments, existence, uniqueness.

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APA Style

Abdelkrim, S., Benchohra, M., Lazreg, J. E., & Henderson, J. (2023). On k-generalized ψ-Hilfer boundary value problems with retardation and anticipation. Advances in the Theory of Nonlinear Analysis and Its Application, 6(2), 173–190.