Controllability of fractional order system with nonlinear term having integral contractor

Abstract

In this paper, controllability results for a class of semilinear control systems of fractional order are established. The nonlinear term is assumed to have an integral contractor which is a weaker condition than the Lipschitz continuity. The existence and uniqueness of mild solution is also proved. MSC 2010 : 93B05, 26A33

Sensitivity analysis of nonlinear fractional order control systems with state delay

“…Hartley studied the finite time controllability of fractional order systems under the condition that lead to a system output remaining at zero with zero input. In [16] Surendra Kumar and N. Sukavanam studied controllability of fractional order system using integral contractor which is a weaker condition than the Lipschitz condition. In [2] K. Balachandran and J. Kokila obtained sufficient conditions for controllability of linear and nonlinear fractional dynamical systems in finite dimensional spaces using Schauders fixed point theorem.…”

“…A c c e p t e d M a n u s c r i p t (16) where L is Lipschitz constant as in assumption (A). We use induction on k to prove this theorem.…”

An exploration of controllability on Hilfer fractional system via integral contractor

“…It leads to some conclusion that the linear dynamical control system can be controlled or not, and if it is controllable, then it drives to find the best control to get the desired result. One can see the literature [9, 11, 14, 17, 22–26] and most studies are there for abstract differential systems in which the operators are defined on a dense domain. Prato and Sinestrari [27] examined numerous examples of semilinear Cauchy problems with non‐dense domain and closed linear operators.…”

“…To get controllability findings for fractional differential equations, George [22] extended the idea of a bounded integral contractor. Subsequently, this idea was used by the authors of Kumar and Sukavanam [23] and Zhu et al [31] to describe controllability findings for the R-L and Caputo fractional evolution equations. The existing results of the HFD were recently explored by Chaudhary and Reich [32] utilizing the integral contractor approach.…”

Controllability of Fractional-Order Directed Complex Networks, with Self Loop and Double Edge Structure

“…Some successful attempts have been undertaken, although recent years the renewed interest has been devoted to the theory of control systems. [30][31][32][33][34][35] Up to now, there are few contributions regarding the controllability of fractional-order complex networks. Motivated by the above discussion, the main aim of the present article is to do some exploitable researches on the controllability of fractional-order complex directed networks.…”