Relative controllability of nonlinear neutral fractional integro‐differential systems with distributed delays in control

Abstract

In this paper, we establish sufficient conditions for the global relative controllability of nonlinear neutral fractional Volterra integro-differential systems with distributed delays in control. The results are obtained by using the MittagLeffler functions and the Schauder fixed-point theorem. Examples are presented to illustrate the results.

Relative Controllability of Linear Difference Equations

“…Concerning the controllability problem, due to the infinite-dimensional nature of the dynamics of neutral functional differential equations and difference equations, several different notions of controllability can be used, such as exact, approximate, spectral, or relative controllability [5,30]. Relative controllability has been originally introduced in the study of control systems with delays in the control input [5,20,27], but this notion has later been extended and used to study also systems with delays in the state [13,29] and in more general frameworks, such as for stochastic control systems [19] or fractional integro-differential systems [2]. The main idea of relative controllability is that, instead of controlling the state x t : [−r, 0] → C d of (1.1), defined by x t (s) = x(t + s), in a certain function space such as C k ([−r, 0], C d ) or L p ((−r, 0), C d ), where r ≥ max j∈ 1,N Λ j , one controls only the final state x(t) = x t (0).…”

Application of Fractional Derivatives in Characterization of ECG graphs

“…Fractional calculus was introduced in 1695. It becomes a rich area of research in the field of basic science and engineering domain from the second half of the twentieth century [1][2][3][4][5][6][7][8][9][10][11]. This paper is dedicated to the latest use of partial calculation that describes ECG graphs using very useful definitions of based on sections by Riemann-Liouville [6,20], Caputo [12,26], and Modified Riemann-Liouville [13,14].…”