Analysis of existence and stability in a fractional-order q-difference model

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Abstract

In this article, our main aim is to explore the existence and uniqueness of solutions for a fractional-order q-equation under a q-integral boundary condition. Employing well-known fixed point theorems, we derive theoretical findings that advance the theory of q-fractional calculus. An example is provided to show the effectiveness of the results, and the stability of the solutions is discussed.

Keywords

q-calculus / Caputo fractional derivative / fixed point theorems / Ulam-Hyers stability / Ulam-Hyers-Rassias stability

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