### Uniqueness of continuous solution to $q$-Hilfer fractional hybrid integro-difference equation of variable order

Published: 25 November 2021

Abstract: In this paper, the authors introduced a novel definition based on Hilfer fractional derivative, which name $q$-Hilfer fractional derivative of variable order. And the uniqueness of solution to $q$-Hilfer fractional hybrid integro-difference equation of variable order of the form \eqref{eq:varorderfrac} with $0 < \alpha(t) < 1$, $0 \leq \beta \leq 1$, and $0 < q < 1$ is studied. Moreover, an example is provided to demonstrate the result.
Keywords: equation / integro / Hilfer / leq / varorderfrac / eqref / name / alpha / beta

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