"Existence and Stability of Nonlinear Implicit Caputo-Exponential Fract" by Mouffak Benchohra, Jamal Eddine Lazreg et al.

Progress in Fractional Differentiation & Applications

Article Title

Existence and Stability of Nonlinear Implicit Caputo-Exponential Fractional Differential Equations

Authors

Mouffak Benchohra, Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, PO Box 89, 22000, Sidi Bel-Abbes, Algeria\\ Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia Follow
Jamal Eddine Lazreg, Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, PO Box 89, 22000, Sidi Bel-Abbes, AlgeriaFollow
Bessem Samet, Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaFollow
Yong Zhou, Faculty of Information Technology, Macau University of Science and Technology, Macau 999078, China\\ Faculty of Mathematics and Computational Science, Xiangtan University, Hunan 411105, ChinaFollow

Author Country (or Countries)

Saudi Arabia

Abstract

In this paper, the existence and stability of solutions for the following fractional problem with Caputo--Exponential fractional derivative are discussed eζ eζ c D0+ ψ (α ) = θ (α , ψ (α ), c D0+ ψ (α )), for each, α ∈ Θ := [0, b], b > 0, 0 < ζ ≤ 1, ψ(0) = ψ0. We use Schauder’s fixed point theorem, the nonlinear alternative of Leray–Schauder type and Banach contraction principle to demonstrate our results. Two examples are provided to demonstrate the relevance of our results.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/pfda/080106

Recommended Citation

Benchohra, Mouffak; Eddine Lazreg, Jamal; Samet, Bessem; and Zhou, Yong (2022) "Existence and Stability of Nonlinear Implicit Caputo-Exponential Fractional Differential Equations," Progress in Fractional Differentiation & Applications: Vol. 8: Iss. 1, Article 6.
DOI: http://dx.doi.org/10.18576/pfda/080106
Available at: https://digitalcommons.aaru.edu.jo/pfda/vol8/iss1/6

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