EXISTENCE RESULTS OF MILD SOLUTIONS FOR IMPULSIVE FRACTIONAL MEASURE DRIVEN DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

The primary focus of this study is the existence and uniqueness of mild solutions for impulsive fractional measure driven differential equations with infinite delay in regular function spaces. First, we rigorously justify the definition of mild solutions for impulsive fractional measure driven differential equations. Then, under conditions of semigroup noncompactness, by utilizing operator semigroup theory, the Kuratowski measure of noncompactness, fixed point theorems, and piecewise estimation techniques, sufficient conditions for the existence of mild solutions are derived. This work extends numerous prior research outcomes, eschewing the need for any priori estimates or noncompactness constraints. Finally, an illustrative example is provided to demonstrate the applicability and efficacy of the theoretical framework.