2025

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Trajectory and null controllability of a control system governed by fractional-order composite relaxation differential equations
(Springer, 2025) Namrata Arya; Ganga Ram Gautam
The purpose of this paper is to study the trajectory controllability (which is said to be the strongest notion rather than other controllabilities) and null controllability of a control system commanded by fractional-order composite relaxation semi-linear differential equation. The linear control system under consideration addresses a classical problem in fluid dynamics, specifically focussing on the dynamics of a particle experiencing unsteady movement within a viscous fluid while subjected to gravitational forces. Initially, we derive the mild solution of the considered control system employing the results on (a, k)-regularised families of bounded linear operator (matrices). Under some appropriate assumptions regarding non-linear terms and by utilising the Gronwall’s inequality, we establish the trajectory controllability and null controllability with constrained controls via fixed point technique. Finally, a few examples are shown to illustrate and explore the applications of the obtained findings. © Indian Academy of Sciences 2025.