Criteria for existence of solutions for a Liouville–Caputo boundary value problem via generalized Gronwall’s inequality

Abstract In this research, we first investigate the existence of solutions for a new fractional boundary value problem in Liouville–Caputo setting with mixed integro-derivative conditions. To do this, Kuratowski’s measure noncompactness and Sadovskii’s fixed point theorem are our tools to reach aim. sequel, discuss continuous dependence on parameters by means generalized Gronwall inequality. Moreover, consider an inclusion version given which study its results endpoint theory. Finally, prepare two simulative numerical examples confirm validity analytical findings.