Existence of solutions for k‐dimensional system of multi‐term fractional q‐integro‐differential equations under anti‐periodic boundary conditions via quantum calculus

Abstract

We prove the existence and uniqueness of solutions for a k-dimensional system of multi-term fractional q-integro-differential equations via anti-periodic boundary conditions by using some well-known tools of fixed point technique such as Arzelà–Ascoli theorem. We firstly give the corresponding Green function for the boundary value problem and some of its attributes. In addition to, we give a numeric method to verify the analysis for checking the existence of a solution of the system. Finally, an interesting example is presented to illustrate the results.

Topics & Concepts