New Results on the Solvability of Abstract Sequential Caputo Fractional Differential Equations with a Resolvent-Operator Approach and Applications

Abdelhamid Mohammed Djaouti, Khellaf Ould Melha and Muhammad Amer Latif ()
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Abdelhamid Mohammed Djaouti: Department of Mathematics and Statistics, Faculty of Sciences, King Faisal University, Hofuf 31982, Al-Ahsa, Saudi Arabia
Khellaf Ould Melha: Department of Mathematics, Faculty of Exact Sciences and Informatics, Hassiba Benbouali University, Ouled Fares, Chlef 02180, Algeria
Muhammad Amer Latif: Department of Mathematics, Faculty of Sciences, King Faisal University, Hofuf 31982, Al-Ahsa, Saudi Arabia

Mathematics, 2024, vol. 12, issue 8, 1-18

Abstract: This paper aims to establish the existence and uniqueness of mild solutions to abstract sequential fractional differential equations. The approach employed involves the utilization of resolvent operators and the fixed-point theorem. Additionally, we investigate a specific example concerning a partial differential equation incorporating the Caputo fractional derivative.

Keywords: Caputo fractional derivative; abstract sequential fractional differential equation; resolvent operators; nonlocal condition (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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