Existence and Ulam–Hyers Stability of a Fractional-Order Coupled System in the Frame of Generalized Hilfer Derivatives

Abdulkafi M. Saeed, Mohammed S. Abdo and Mdi Begum Jeelani
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Abdulkafi M. Saeed: Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
Mohammed S. Abdo: Department of Mathematics, Hodeidah University, Al-Hudaydah, Yemen
Mdi Begum Jeelani: Department of Mathematics, Imam Mohammad Ibn Saud Islamic University, Riyadh 11564, Saudi Arabia

Mathematics, 2021, vol. 9, issue 20, 1-17

Abstract: In this research paper, we consider a class of a coupled system of fractional integrodifferential equations in the frame of Hilfer fractional derivatives with respect to another function. The existence and uniqueness results are obtained in weighted spaces by applying Schauder’s and Banach’s fixed point theorems. The results reported here are more general than those found in the literature, and some special cases are presented. Furthermore, we discuss the Ulam–Hyers stability of the solution to the proposed system. Some examples are also constructed to illustrate and validate the main results.

Keywords: ? -Hilfer fractional derivative; fractional coupled system; existence and stability of solutions; fixed point theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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