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1 2023

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Application of fractional quantum calculus on coupled hybrid differential systems within the sequential Caputo fractional q-derivatives

Alzabut Jehad, Houas Mohamed, Abbas Mohamed I.

Demonstratio Mathematica

2023

Vol. 56, nr 1

art. no. 20220205

In the current manuscript, we combine the q-fractional integral operator and q-fractional derivative to investigate a coupled hybrid fractional q-differential systems with sequential fractional q-derivatives. The existence and uniqueness of solutions for the proposed system are established by means of Leray-Schauder’s alternative and the Banach contraction principle. Furthermore, the Ulam-Hyers and Ulam-Hyers-Rassias stability results are discussed. Finally, two illustrative examples are given to highlight the theoretical findings.