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

Samei Mohammad Esmael (Department of Mathematics, Faculty of Science, Bu-Ali Sina University, Hamedan, Iran), mesamei@basu.ac.ir, mesamei@gmail.com

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 existence 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.

Keywords: Positive solutions, Caputo q-derivative, fixed point, singularity, sum fractional q-differential equations