On Solutions of the Nonlocal Generalized Coupled Langevin‐Type Pantograph Systems

This paper concentrates on the analysis of a category of coupled Langevin‐type pantograph differential equations involving the generalized Caputo fractional derivative with nonlocal conditions. We conduct this analysis in two cases for the second member in the nonlinear function; in other words, for the real space and an abstract Banach space Θ. To prove the existence and uniqueness of solutions to our problems, we used different types of the fixed point theorems attributed to Banach, Schaefer and Darbo, along with the measure of noncompactness. Lastly, we provide examples to illustrate our findings.