On a system of fractional q-differential inclusions via sum of two multi-term functions on a time scale

Abstract

Abstract Nowadays most researchers have been focused on fractional calculus because it has been proved that fractional derivatives could describe most phenomena better than usual derivations. Numerical parts of fractional calculus such as q-derivations are considered by researchers. In this work, our aim is to review the existence of solution for an m-dimensional system of fractional q-differential inclusions via sum of two multi-term functions under some boundary conditions on the time scale T t 0 = { t : t = t 0 q n } ∪ { 0 } $\mathbb{T}_{t_{0}}= \{ t : t =t_{0}q^{n}\}\cup\{0\}$ , where n ≥ 1 $n\geq1$ , t 0 ∈ R $t_{0} \in\mathbb{R}$ , and q ∈ ( 0 , 1 ) $q \in(0,1)$ . By using the Banach contraction principle and some sufficient conditions, we guarantee the existence of solutions for the system of q-differential inclusions. Also, we provide an example, some algorithms, and a figure to illustrate our main result.

Keywords

• Multi-term function
• Sum boundary value condition
• Caputo q-derivative
• Riemann–Liouville q-derivative
• Time scale