"This paper deals with some existence results for a class of implicit fractional q-difference equations. The are based on the fi xed point theory in Banach spaces and concept measure noncompactness. An illustrative example is given last section."

*Correspondence: [email protected]; [email protected] 3Department of Mathematics, Zanjan Branch, Islamic Azad University, Zanjan, Iran Full list of author information is available at the end of the article Abstract In this paper, some new generalization of Darbo’s fixed point theorem is proved by using a F(ψ ,φ)-contraction in terms of a measure of noncompactness. Our result extends to obtai...

This article is entirely devoted to the application of measure noncompactness defined in Holder space. Here emphasis on study nonlinear functional integral equation with changed arguments. Precisely, existence a solution obtained by employing Darbo fixed point theorem under certain hypotheses. Finally, we provide tangible example which supports our results.

We investigate the existence of solutions for a nonlinear fractional differential inclusion in sense hybrid Caputo-proportional derivatives (HCPFDs) Banach spaces. The main result is discussed by using set-valued concern from Mönch fixed-point theorem along with Kuratowski measure noncompactness. present an example to demonstrate theoretical findings.