Mittag–Leffler stability analysis of nonlinear fractional-order systems with impulses

On Ulam's type stability for a class of impulsive fractional differential equations with nonlinear integral boundary conditions

“…This concept was introduced in the mid of 19th century and now it is a well-explored area of research. Further, about the stability of functional equations, ordinary differential equations and FDEs for some recent work, we recommend the readers to study [3,3,14,30,36]. Further, to know about the recent contribution, we refer to [4, 5, 8, 10-12, 15, 17, 18, 21, 26, 27, 31, 33, 35, 37, 38].…”

Finite‐Time Guaranteed Cost Control of Caputo Fractional‐Order Neural Networks

“…As is well known, stability is one of the most concerned problems for any dynamic system . For fractional‐order systems, many interesting results on the stability analysis in the sense of Lyapunov, including asymptotic stability, uniform stability, stability and Hopf Bifurcation analysis and Mittag–Leffler stability have been reported in the literature (see and the reference therein). It should be noted that Lyapunov stability deals with the asymptotic behavior of a system over a sufficiently long‐time interval.…”

Analysis of a Class of Fractional Nonlinear Multidelay Differential Systems

“…A function ∈ is a solution of inequality (26) if and only if there exists a function ∈ (which depend on ) such that Proof. Let ∈ ([− , ], R) be a solution of inequality (26) and ( ) be a solution of…”

“…Recently, considerable attention has been given to the control and stability of fractional differential equations; one can refer to via Ulam's type stability concepts and the references therein. We also note that there are some contributions on Mittag-Leffler stability of fractional order systems and stabilization [26][27][28][29]. We remark that there are some difference between the concept of MittagLeffler stability and Ulam-Hyers-Mittag-Leffler stability.…”