A study of a coupled system involving tempered Caputo derivatives with respect to functions
摘要
The goal of this manuscript is to analyze a class of coupled systems driven by the Caputo tempered fractional derivative with respect to a function in a Banach space framework. Firstly, a Gronwall’s inequality with singular type is generalized in the coupled context. Secondly, the nonlinear alternative for condensing maps is used to deduce the compactness of the set of global solutions. An example is given to illustrate our findings.