Employing Kuratowski measure of non-compactness for positive solutions of system of singular fractional q-differential equation with numerical effects

Abstract

In this work, we investigate the existence of solutions for the system of two singular fractional q-differential equation under integral boundary conditions.  which therein we use the concept of Caputo fractional q-derivative and fractional Riemann-Liouville type q-integral. Some new sxistence results are obtained by applying Krattowski measure on non-compactness sets. Also, the Darbo's fixed point theorem and the Lebesgue dominated convergence theorem are the main tools in deriving our proofs Lastly, we present an examples illustrating the primary effects.