An analysis concerning to the existence of mild solution for Hilfer fractional neutral evolution system on infinite interval

Abstract

In this article, we focus on the new class of neutral Hilfer fractional differential equations on infinite interval in Banach space. The results are obtained with the help of the theory of fractional calculus, mild solutions, the fixed point theorem, semigroup theory, and infinite interval. First, we introduce a mild solution for neutral Hilfer fractional differential equations. Then, we prove the existence of a mild solution for the neutral Hilfer fractional differential equations. Finally, an example is provided to illustrate the obtained results.