On implicit boundary value problems with Caputo type modification of the Erdélyi–Kober fractional differential equations

Abstract

This article deals with the existence of solutions to a boundary value problem for the Caputo type modification of the Erdélyi–Kober fractional differential equations. Our primary results are demonstrated by combining the fixed point theorems of Darbo and Mönch with the approach of measures of noncompactness. Furthermore, an example is provided to highlight the applicability of our findings.