Trajectory controllability of higher-order fractional neutral stochastic system with non-instantaneous impulses via state-dependent delay with numerical simulation followed by hearth wall degradation process

Nowadays, engineers and biochemical industries have benefited greatly from controllability analysis and its computational methods. In this paper, the strongest notion of controllability called trajectory controllability (TC) of higher-order fractional neutral stochastic integrodifferential systems (FNSIDEs) with non-instantaneous impulsive (NI) via state-dependent delay is studied. The existence and uniqueness of solutions are proved in the infinite-dimensional space by using M & ouml;nch-type fixed-point theorem with the Hausdroff measure of noncompactness without compactness assumption on the semigroup. Further, the control problem is considered to establish TC results for FNSIDEs with NII. Then after, a fractional neutral stochastic model is discussed in the example section which is extended by the numerical simulation and the optimization technique supported by the Nelder-Mead method is used to identify the control that makes the state equations track a certain control. Finally, the remaining usable life, which can be described by either the probability density function or the point estimate of the mathematical expectation under certain specific stochastic assumptions, is typically defined and a case study on certain hearth wall degradation processes to validate the proposed method in practice.