Abstract
In this paper, our main purpose is to study a class of higher-order fractional stochastic delay differential equations (FSDDEs). We first define a more generalized delay Grammian matrix involving delayed matrix functions, and then we obtain the relatively exact controllability of linear higher-order FSDDEs by using such matrix. Subsequently, by constructing a suitable control function, we discuss relatively exact controllability of the nonlinear addressed equations. The results we presented are based on a new approach, Carathéodory approximation, which differs from previous literature. The main results are obtained by using fractional calculus, nonlinear analysis, Jensen inequality, Grönwall-Bellman inequality, Hölder inequality, Bihari inequality and Burkholder-Davis-Gundy inequality. Finally, the theoretical conclusions are supported through examples.
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