Stability analysis of fractional-order linear neutral delay differential–algebraic system described by the Caputo–Fabrizio derivative

Abstract

This paper is concerned with the asymptotic stability of linear fractional-order neutral delay differential–algebraic systems described by the Caputo–Fabrizio (CF) fractional derivative. A novel characteristic equation is derived using the Laplace transform. Based on an algebraic approach, stability criteria are established. The effect of the index on such criteria is analyzed to ensure the asymptotic stability of the system. It is shown that asymptotic stability is ensured for the index-1 problems provided that a stability criterion holds for any delay parameter. Also, asymptotic stability is still valid for higher-index problems under the conditions that the system matrices have common eigenvectors and each pair of such matrices is simultaneously triangularizable so that a stability criterion holds for any delay parameter. An example is provided to demonstrate the effectiveness and applicability of the theoretical results.

Further results on finite-time stability of neutral nonlinear multi-term fractional order time-varying delay systems

“…The system (47) can be reduced to [37], ((9) for case n = 1, τ N 1 = 0, A N 2 = B 1 = 0, C = 0) and [38], (1) assuming that τ N 1 = 0, A N 2 = B 1 = 0, C = 0, f = 0. It is easily check that obtained criteria (29), (48) are more general.…”

“…Particularly, some authors have devoted attention to stability and control issues of the neutral TDS (NTDS) integer and fractional order [21][22][23][24][25][26][27][28][29][30]. Integer order NTDS in mechanical problems were presented in [21,22]; the stability chart of an elastic beam was obtained in [21] and the problem of ship rolling with control based on values of delayed acceleration was considered in [22].…”

A Fractional Order Delay Differential Model for Survival of Red Blood Cells in an Animal: Stability Analysis

“…Hence from equation ( 17), we get du dτ > 0 on each of the critical surfaces τ 1 (n) and τ 2 (n). This implies that there does not exist any eigen value with negative real part across the critical surfaces ( 13) and (14). Also the equilibrium point is stable for τ = 0 when pf (N * ) − μ < 0.…”

“…Khalouta and Kade [11] have studied the solution of the fractional bratu-type equation by fractional residual power series method. Deng et al [12], Čermák et al [13], Sawoor [14] and Chartubapan et al [15] have done the stability analysis of fractional differential equations. Several researchers such as Radha and Balamuralitharan [16] and Preethilatha et al [17] have proposed different types of fractional order time delay biological models and have done the stability analysis of the respective models.…”

Analysis of the Mathematical Modelling of COVID-19 by Using Mild Solution with Delay Caputo Operator

“…The method of [21,22] is noteworthy in this respect. We examined a fractional variant of the novel coronavirus model 1 in this manuscript and employed the concept of a fractional CF derivative [23], which is now being used by many scientists to examine a wide variety of issues in biological and physical sciences; for example, [24][25][26]. The concept of a CF derivative has already been used numerous times to explain the motion of different highly infectious infections [27,28].…”