Journal of Advanced Analysis and Applications
Volume 1, Issue 1 (2026), Pages 54–68

On Nonlinear Caputo Tempered Impulsive Implicit Fractional Problems
Authors: Soufyane Bouriah1, Abdelkrim Salim2,*, Rosana Rodríguez-López3, and Mouffak Benchohra4

1Department of Mathematics, Faculty of Exact Sciences and Informatics, University Hassiba Benbouali of Chlef, Algeria
2Faculty of Technology, Hassiba Benbouali University of Chlef, P.O. Box 151, Chlef 02000, Algeria
3CITMAga, and Departamento de Estatística, Análise Matemática e Optimización, Facultade de Matemáticas, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
4Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, P.O. Box 89, Sidi Bel-Abbes 22000, Algeria
*Correspondence: Email: salim.abdelkrim@yahoo.com | a.salim@univ-chlef.dz

Abstract. The main goal of this paper is to study the existence and uniqueness of impulsive implicit fractional differential equation involving the Caputo tempered (C-T) fractional derivative depending on Riemann-Liouville (R-L) tempered fractional integral. The results are based upon the Banach contraction principle, and Krasnoselskii’s fixed point theorem. Furthermore, several illustrations are presented to demonstrate the plausibility of our results.

Keywords: fixed point; existence; uniqueness; tempered fractional operators; integro-differential problems

MSC (2020): 34A08, 34B10, 34B40

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Submitted: January 10, 2026 / Accepted: April 9, 2026 / Published: April 19, 2026

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How to cite: S. Bouriah et al., On nonlinear Caputo tempered impulsive implicit fractional problems,
Journal of Advanced Analysis and Applications, 1(1) (2026), 54–68.
DOI: https://doi.org/10.66745/jaaa.v1i1.004

This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). https://creativecommons.org/licenses/by/4.0/

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