On Implicit Neutral Tempered ψ-Caputo Fractional Differential Equations with Delay via Densifiability Techniques

Open Access

Original research article

Author(s):

Nawal Bettayeb^b, Abdelkrim Salim^a,b, Jamal Eddine Lazreg^a, Mouffak Benchohra^a

^aLaboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, P.O. Box 89, Sidi Bel-Abbes 22000, Algeria
^bFaculty of Technology, Hassiba Benbouali University of Chlef, P.O. Box 151, Chlef 02000, Algeria

Advances in the Theory of Nonlinear Analysis and its Applications 7 (5), 44-65.

Received: September 20, 2023

Accepted: November 28, 2023

Published: December 24, 2023

Abstract

This article is a subject about the existence results for a class of tempered ψ–Caputo fractional differential equations. These problems encompass nonlinear implicit neutral fractional differential equations involving various types of delays, including finite, infinite, and state-dependent delays. The results are based on the concept of the degree of non-densifiability (DND) combined with Darbo-type fixed point theorem on Banach space using the properties of the phase space. In the last section, we provide some examples to illustrate our obtained results.

Keywords: Tempered ψ–Caputo fractional derivative; Implicit neutral problem; Existence; Degree of nondensifiability; Finite delay; Infinite delay; State-dependent delay; Fixed point.

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APA Style

Bettayeb, N., Salim, A., Lazreg, J. E., & Benchohra, M. (2023). On implicit neutral tempered ψ-Caputo fractional differential equations with delay via densifiability techniques. Adv. Theory Nonl. Anal. Appl , 7 (5), 44-65.