The exponential nature and solvability of stochastic multi-term fractional differential inclusions with Clarke’s subdifferential

Abstract

This study explores a new class of stochastic multi-term fractional differential inclusions with the Clarke subdifferential involving the Rosenblatt process. The presence and uniqueness of a solution are determined by the successive approximation approach in combination with the stochastic analysis methodology and the resolvent operators. Furthermore, new sufficient conditions are given to ensure the exponential decay of the mild solution without Lipschitz conditions on non-linear terms. We have also provided an example to validate the obtained results.