In this paper, we present a new class of functions, called \(\mu \) -Stepanov-like pseudo S-asymptotically \((\omega,c)\) -periodic functions, which are distinguished by their reliance on measure-based properties. These functions are utilized to study evolution equations in Banach spaces. We begin by providing a precise definition of this class and exploring its principal theoretical features, such as completeness, convolution, and superposition, in an abstract setting. We then establish the existence and uniqueness of mild solutions for a class of Weyl-type fractional integro-differential equations by applying Banach’s fixed point theorem. To illustrate the effectiveness of the results, a concrete example is provided.
