Existence of mild solutions for a multi-term fractional differential equation via ψ-(γ,σ)-resolvent operators

Abstract

In this paper, we consider a multi-term fractional differential equation involving the [Formula: see text]-Caputo fractional derivative. Under some suitable hypotheses, we prove that our proposed problem has at least one mild solution expressed in terms of the [Formula: see text]-[Formula: see text]-resolvent. As an application, we provide a suitable example at the end of this work to illustrate our theoretical results.