This paper presents a novel category of functions \((\mu _{1},\mu _{2})\) -pseudo S-asymptotically \((\omega ,c)\) -periodic, which are characterized by their incorporation of dual measures. These functions are applied to the investigation of evolution equations within Banach spaces. The research initially defines these functions and explores crucial theoretical attributes, including theorems on completeness, convolution, and superposition in abstract spaces. It subsequently establishes the existence and uniqueness of mild solutions for Weyl fractional integrodifferential equations by utilizing these functions. Lastly, an example is presented to demonstrate their practical use.
