Title: Uniqueness and Ulam stability for implicit fractional q-difference equations via Picard operators theory

Authors: Saïd Abbas; Mouffak Benchohra; John R. Graef; Nadjet Laledj

Addresses: Department of Electronics, Tahar Moulay University of Saïda, P.O. Box 138, EN-Nasr, 20000 Saïda, Algeria ' Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbès, P.O. Box 89, Sidi Bel-Abbès 22000, Algeria ' Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN, 37403, USA ' Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbès, P.O. Box 89, Sidi Bel-Abbès 22000, Algeria

Abstract: The authors are concerned with the uniqueness of solutions and Ulam type stability results for implicit Caputo fractional q-difference equations. Coupled systems of implicit fractional q-difference equations are also considered. Their results are obtained by using the Picard operator theory due to Rus. An illustrative example is given in the last section of the paper.

Keywords: fractional q-difference equation; coupled system; implicit; weekly Picard operator; fixed point equation; Ulam-Hyers-Rassias stability; fixed point.

DOI: 10.1504/IJDSDE.2023.129515

International Journal of Dynamical Systems and Differential Equations, 2023 Vol.13 No.1, pp.58 - 75

Accepted: 31 Mar 2022
Published online: 13 Mar 2023 *

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