Unique Solutions for Caputo Fractional Differential Equations with Several Delays Using Progressive Contractions

Cemil Tunç and Fahir Talay Akyildiz ()
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Cemil Tunç: Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yıl University, 65080 Van, Turkey
Fahir Talay Akyildiz: Department of Mathematics and Statistics, Faculty of Sciences, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11564, Saudi Arabia

Mathematics, 2024, vol. 12, issue 18, 1-15

Abstract: We take into account a nonlinear Caputo fractional-order differential equation including several variable delays. We examine whether the solutions to the Caputo fractional-order differential equation taken under consideration, which has numerous variable delays, are unique. In the present study, first, we will apply the method of progressive contractions, which belongs to T.A. Burton, to Caputo fractional-order differential equation, including multiple variable delays, which has not yet appeared in the relevant literature by this time. The significant point of the method of progressive contractions consists of a very flexible idea to discuss the uniqueness of solutions for various mathematical models. Lastly, we provide two examples to demonstrate how this paper’s primary outcome can be applied.

Keywords: unique solution; Caputo fractional derivative; differential equation; several variable delays; progressive contractions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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