Nonlocal initial value problems for differential equations with Hilfer fractional derivative

In this paper, we discuss the existence of solutions to nonlocal initial value problem for differential equations with Hilfer fractional derivative. To begin with, we establish an equivalent mixed type integral equation for our problem. Then, we utilize basic properties of Hilfer fractional calculus and fixed point methods to derive three fundamental existence results in the weighted space of continuous functions. Some examples are given to illustrate our results.