Related papers: Stability Analysis of Short Memory Fractional Diff…
This paper deals with stability of a certain class of fractional order linear and nonlinear systems. The stability is investigated in the time domain and the frequency domain. The general stability conditions and several illustrative…
Fractional differential equations model processes with memory effects, providing a realistic perspective on complex systems. We examine time-delayed differential equations, discussing first-order and fractional Caputo time-delayed…
We develop a fully discrete scheme for time-fractional diffusion equations by using a finite difference method in time and a finite element method in space. The fractional derivatives are used in Caputo sense. Stability and error estimates…
This work is concerned with the stability properties of linear stochastic differential equations with random (drift and diffusion) coefficient matrices, and the stability of a corresponding random transition matrix (or exponential…
In this paper, we prove a theorem of linearized asymptotic stability for fractional differential equations with a time delay. More precisely, using the method of linearization of a nonlinear equation along an orbit (Lyapunov's first…
In the paper we deal with linear fractional control problems with constant delays in the state. Single-order systems with fractional derivative in Caputo sense of orders between 0 and 1 are considered. The aim is to introduce a new…
Transport equations with a nonlocal velocity field have been introduced as a continuum model for interacting particle systems arising in physics, chemistry and biology. Fractional time derivatives, given by convolution integrals of the…
In this paper, we are interested in the study of a problem with fractional derivatives having boundary conditions of integral types. The problem represents a Caputo type advection-diffusion equation where the fractional order derivative…
A memristor is a nonlinear two-terminal electrical element that incorporates memory features and nanoscale properties, enabling us to design very high-density artificial neural networks. To enhance the memory property, we should use…
In this paper we present a new type of fractional operator, the Caputo-Katugampola derivative. The Caputo and the Caputo-Hadamard fractional derivatives are special cases of this new operator. An existence and uniqueness theorem for a…
Stability of retarded differential equations is closely related to the existence of Lyapunov-Krasovskii functionals. Even if a number of converse results have been reported regarding the existence of such functionals, there is a lack of…
This paper is devoted to the study of the well-posedness of a singular nonlinear fractional pseudo-hyperbolic system. The fractional derivative is described in Caputo sense. The equations are supplemented by classical and nonlocal boundary…
This paper deals with the initial value problem for the multi-term fractional differential equation. The fractional derivative is defined in the Caputo sense. Firstly the initial value problem is transformed into a equivalent Volterra-type…
The persistence theory has been employed by several authors in order to study persistence properties of dynamical systems generated by ordinary differential equations or maps across diverse disciplines. In this note, the author discusses a…
This paper establishes a far-reaching connection between the Finite-Difference Time-Domain method (FDTD) and the theory of dissipative systems. The FDTD equations for a rectangular region are written as a dynamical system having the…
In this paper, we consider a class of the Caputo fractional stochastic differential equations of fractional order $\alpha \in (\frac{1}{2},1]$. Our aim is to analyze of the continuous dependence of solutions on the fractional order…
In this work we argue about the Lesche stability of some systems, that are motivated by the use of fractional derivatives.
This paper studies input-to-state stability for hybrid systems with memory, which models hybrid dynamics affected by time delays. Using both Lyapunov-Razumikhin functions and Lyapunov-Krasovskii functionals, Lyapunov-based sufficient…
The main purpose of this paper is to study the special fractional-order Chen-Lee system, using the Caputo fractional derivatives. For this fractional model we investigate the existence and uniqueness of solution of initial value problem,…
This work presents an analytical and computational study of fractional-order delay differential equations formulated using both the conformable and Caputo derivatives. For the conformable case, we develop the associated integral,…