A novel delay-dependent asymptotic stability conditions for differential and Riemann-Liouville fractional differential neutral systems with constant delays and nonlinear perturbation

The novel delay-dependent asymptotic stability of a differential and Riemann-Liouville fractional differential neutral system with constant delays and nonlinear perturbation is studied. We describe the new asymptotic stability criterion in the form of linear matrix inequalities (LMIs), using the application of zero equations, model transformation and other inequalities. Then we show the new delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral system with constant delays. Furthermore, we not only present the improved delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral system with single constant delay but also the new delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral equation with constant delays. Numerical examples are exploited to represent the improvement and capability of results over another research as compared with the least upper bounds of delay and nonlinear perturbation.This work is supported by Science Achievement Scholarship of Thailand (SAST), Research and Academic Affairs Promotion Fund, Faculty of Science, Khon Kaen University, Fiscal year 2020 and National Research Council of Thailand and Khon Kaen University, Thailand (6200069)

On the Nonlinear Impulsive Ψ\Psi--Hilfer Fractional Differential Equations

In this paper, we consider the nonlinear $\Psi$-Hilfer impulsive fractional differential equation. Our main objective is to derive the formula for the solution and examine the existence and uniqueness of results. The acquired results are extended to the nonlocal $\Psi$-Hilfer impulsive fractional differential equation. We gave an applications to the outcomes we procured. Further, examples are provided in support of the results we got.Comment: 2

Fractional Order Version of the HJB Equation

We consider an extension of the well-known Hamilton-Jacobi-Bellman (HJB) equation for fractional order dynamical systems in which a generalized performance index is considered for the related optimal control problem. Owing to the nonlocality of the fractional order operators, the classical HJB equation, in the usual form, does not hold true for fractional problems. Effectiveness of the proposed technique is illustrated through a numerical example.Comment: This is a preprint of a paper whose final and definite form is with 'Journal of Computational and Nonlinear Dynamics', ISSN 1555-1415, eISSN 1555-1423, CODEN: JCNDDM. Submitted 28-June-2018; Revised 15-Sept-2018; Accepted 28-Oct-201

Generalized Mittag-Leffler stability of fractional impulsive differential system

This paper establishes sufficient conditions for Generalized Mittag-Leffler stability of a class of impulsive fractional differential system with Hilfer order. The analysis extends through both, instantaneous and non-instantaneous impulsive conditions. The theory utilizes continuous Lyapunov functions, to ascertain the stability conditions. An example is given discussing for various ranges

Practical stability for fractional impulsive control systems with noninstantaneous impulses on networks

This paper investigates practical stability for a class of fractional-order impulsive control coupled systems with noninstantaneous impulses on networks. Using graph theory and Lyapunov method, new criteria for practical stability, uniform practical stability as well as practical asymptotic stability are established. In this paper, we extend graph theory to fractional-order system via piecewise Lyapunov-like functions in each vertex system to construct global Lyapunov-like functions. Our results are generalization of some known results of practical stability in the literature and provide a new method of impulsive control law for impulsive control systems with noninstantaneous impulses. Examples are given to illustrate the effectiveness of our result