Temporal periodic solutions for fractional evolution equations with nonlinear source terms

This work addresses a class of nonlinear fractional evolution equations involving time-periodic conditions. Our objective is to investigate the existence and uniqueness of weak periodic solutions to the proposed model within an appropriate framework. We introduce a novel formulation of the fractional periodic problem, transforming it into an equivalent fixed point problem within a well-suited Banach space. Through the use of monotone operator theory and Leray Schauder's topological degree, we thoroughly examine the existence and uniqueness of weak periodic solutions to the studied models.