Analysis of fractional stochastic evolution equations by using Hilfer derivative of finite approximate controllability

Abstract

The approximate controllability of a class of fractional stochastic evolution equations (FSEEs) are discussed in this study utilizes the Hilbert space by using Hilfer derivative. For different approaches, we remove the Lipschitz or compactness conditions and merely have to assume a weak growth requirement. The fixed point theorem, the diagonal argument, and approximation methods serve as the foundation for the study. The abstract theory is demonstrated using an example. A conclusion is given at the end.

Keywords

• stochastic calculus
• hilfer derivative
• finite approximate controllability
• semi-group
• fixed point theory
• stochastic evolution equations