Some analytical and numerical results for a fractional q-differential inclusion problem with double integral boundary conditions

Abstract

Abstract In this work, we study a q-differential inclusion with doubled integral boundary conditions under the Caputo derivative. To achieve the desired result, we use the endpoint property introduced by Amini-Harandi and quantum calculus. Integral boundary conditions were considered on time scale T t 0 = { t 0 , t 0 q , t 0 q 2 , … } ∪ { 0 } $\mathcal{T}_{t_{0}}=\{t_{0},t_{0}q,t_{0}q^{2}, \ldots\}\cup \{0\}$ . To better evaluate the validity of our results, we provided an example, some graphs, and tables.

Keywords

• q-differential inclusion problem
• Fixed point
• Numerical results
• The Caputo derivative