J. Nonl. Evol. Equ. Appl. 2022 (6), pp. 105-126, published on April 11, 2023:

On k-generalized ψ-Hilfer Impulsive Boundary Value Problem with Retarded and Advanced Arguments in Banach Spaces

Abdelkrim Salim(a), Mouffak Benchohra(a), Jamal Eddine Lazreg(a) and Yong Zhou(b).

(a) Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, P.O. Box 89 Sidi Bel Abbes 22000, Algeria
(a) Faculty of Mathematics and Computational Science, Xiangtan University

Received on April 26, 2022
Accepted on June 9, 2022

Communicated by Gaston M. N'Guérékata

Abstract.  This paper deals with the existence and uniqueness results for a class of boundary value problem for implicit nonlinear fractional differential equations with with instantaneous impulses and k-Generalized ψ-Hilfer fractional derivative involving both retarded and advanced arguments. The result are based on Mönch fixed point theorem associated with the technique of measure of noncompactness. An illustrative example is provided to indicate the applicability of our results.
Keywords: ψ-Hilfer fractional derivative, k-generalized ψ-Hilfer fractional derivative, impulsions, retarded arguments, Banach Space, advanced arguments, existence, uniqueness.
2010 Mathematics Subject Classification:   34A08, 26A33, 34A12.
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