Trajectory Controllability of Fractional Integro‐Differential Systems in Hilbert Spaces

Abstract

In this paper, sufficient conditions for trajectory controllability of nonlinear fractional integro‐differential systems involving Caputo fractional derivative of order α∈(1,2] in finite and as well as in infinite dimensional Hilbert spaces are obtained. Our tools of study include set‐valued functions, theory of monotone operators and α‐order cosine family of operators. The main results are well illustrated with the aid of examples.

Approximate controllability of higher order Riemann–Liouville fractional systems via cosine family

“…In last two decades, the existence and controllability results for the differential equations involving Caputo derivatives have been presented in many papers (see [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33] and references therein). However, only few articles are reported on the controllability of Riemann-Liouville fractional differential equations.…”

Trajectory Controllability of Clarke Subdifferential-Type Conformable Fractional Stochastic Differential Inclusions with Non-Instantaneous Impulsive Effects and Deviated Arguments

“…In [38], the authors looked into whether second-order evolution systems in Banach space with diverging arguments and impulses are T-controllable. In the context of the Caputo fractional derivative of order α ∈ (1, 2], the T-controllability of fractional integrodifferential equations was established in [39]. The approximation and T-controllability of fractional SDEs with non-instantaneous impulses and Poisson jumps were also addressed in [40] using the same techniques.…”

Approximate and trajectory controllability of fractional stochastic differential equation with non‐instantaneous impulses and Poisson jumps

“…In trajectory controllability problems, we look for a control function that steers the system along a prescribed trajectory rather than a control function steering a given initial state to the desired final state. For more recent works on trajectory controllability, one may see [26‐29] and the references cited therein. Malik and George [26] established the trajectory controllability for nonlinear fractional differential equations.…”

“…Malik and George [26] established the trajectory controllability for nonlinear fractional differential equations. Govindaraj and George [28] discussed the trajectory controllability of fractional integro‐differential equations. Moreover, approximate and trajectory controllability results on non‐instantaneous impulses are rarely available in the literature, which serves as a motivation for our research work in this paper.…”