Existence of solutions for impulsive differential models on half lines involving Caputo fractional derivatives

In this article, we establish existence results of at least one solution for two classes of initial value problems of nonlinear impulsive fractional differential models on half lines involving Caputo fractional derivatives. Our analysis rely on the well known fixed point theorem of Schauder and nonlinear alternative of Leray–Schauder type.

► We construct properly Banach spaces and suitable operators and prove technically that the operator is completely continuous. ► The results and the methods that are full of new ideas in this paper are useful for scientists in nonlinear area. ► We establish existence results of solution for IVPs of impulsive fractional differential models on half lines.