Pure mathematics

Applied mathematics

Evolution equation

Mathematics

Mathematical analysis

Semigroup

Interval (graph theory)

Combinatorics

Fractional calculus

In this paper, we investigate infinite interval problems for the fractional evolution equations with Hilfer fractional derivative. By using the generalized Ascoli–Arzelà theorem and some new techniques, we prove the existence of mild solutions of Hilfer fractional evolution equations when the semigroup is compact as well as noncompact. In addition, an example is provided to illustrate the results.

Infinite Interval Problems for Fractional Evolution Equations