Uniqueness of continuous solution to $q$-Hilfer fractional hybrid integro-difference equation of variable order
Open Access
- 25 November 2021
- journal article
- Published by SABA Publishing in Journal of Mathematical Analysis and Modeling
- Vol. 2 (3), 88-98
- https://doi.org/10.48185/jmam.v2i3.421
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.