Employing Kuratowski Measure of Non-compactness for Positive Solutions of System of Singular Fractional q-Differential Equations with Numerical Effects

In this work, we investigate the existence of solutions for the system of two singular fractional q-differential equations under integral boundary conditions via the concept of Caputo fractional q-derivative and fractional Riemann-Liouville type q-integral. Some new sxistence results are obtained by applying Krattowski measure of non-compactness. 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 example illustrating the primary effects.