Approximate Controllability of Fractional Backward Stochastic Differential Inclusions with Order 1/2 < P < 1

Abstract

In this paper, fractional backward stochastic differential equations are extended to multivalued forms. Since the problem of approximate controllability of the obtained fractional backward stochastic differential inclusions has not yet been addressed in the literature, we focus on the approximate controllability of these systems. The study’s main results, such as existence of the mild solution and approximate controllability for fractional backward stochastic differential inclusions, have been proven through fractional calculus, Bohnenblust-Karlin Theorem, and appropriate conditions. © 2025 Elsevier B.V., All rights reserved.