A Study of Positive Solutions for Semilinear Fractional Measure Driven Functional Differential Equations in Banach Spaces

Abstract

In this paper, we deal with the delayed measure differential equations with nonlocal conditions via measure of noncompactness in ordered Banach spaces. Combining (β,γk)-resolvent family, regulated functions and fixed point theorem with respect to convex-power condensing operator and measure of noncompactness, we investigate the existence of positive mild solutions for the mentioned system under the situation that the nonlinear function satisfies measure conditions and order conditions. In addition, we provide an example to verify the rationality of our conclusion.

Keywords

• regulated functions
• measure driven equations
• positive mild solutions
• convex-power condensing operator