Fractional stochastic differential equations and degree theory: a unified perspective

This research focuses on the existence and uniqueness of solutions for a novel class of tempered φ-Caputo stochastic fractional differential equations. The analysis is grounded in foundational concepts from fractional calculus and topological degree theory. We establish the existence of solutions by employing the topological degree approach for condensing maps. Furthermore, the uniqueness of solutions is derived using the Banach fixed point theorem. To validate our theoretical results, illustrative examples are presented.