Related papers: Fractional Discrete Systems with Sequential h-diff…
Recently, a new fractional derivative called the conformable fractional derivative is given on based basic limit definition derivative in [4]. Then, the fractional versions of chain rules, exponential functions, Gronwalls inequality,…
This paper is devoted to studying three-dimensional non-commensurate fractional order differential equation systems with Caputo derivatives. Necessary and sufficient conditions are for the asymptotic stability of such systems are obtained.
In this paper we study linear and nonlinear fractional differential equations involving the Caputo fractional derivative with Mittag-Leffler non-singular kernel of order $0<\alpha<1.$ We first obtain a new estimate of the fractional…
In this paper, a homogeneous system of n $\alpha$-order linear fractal differential equation is defined and the set of its fundamental solutions through the corresponding Wronskian matrix is described. Finally, the solutions of some…
This paper deals with fractional-order controlled systems and fractional-order controllers in the frequency domain. The mathematical description by fractional transfer functions and properties of these systems are presented. The new ways…
In this paper we develop a fractional Hamiltonian formulation for dynamic systems defined in terms of fractional Caputo derivatives. Expressions for fractional canonical momenta and fractional canonical Hamiltonian are given, and a set of…
Fractional action-like variational problems have recently gained importance in studying dynamics of nonconservative systems. In this note we address multi-dimensional fractional action-like problems of the calculus of variations.
In this paper we consider the linearized version of a system of partial differential equations arising from a fluid-structure interaction model. We prove the existence and the uniqueness of the solution under natural regularity assumptions.
In this paper we consider a reduction of a non-homogeneous linear system of first order operator equations to a totally reduced system. Obtained results are applied to Cauchy problem for linear differential systems with constant…
This contribution deals with identification of fractional-order dynamical systems. System identification, which refers to estimation of process parameters, is a necessity in control theory. Real processes are usually of fractional order as…
We consider a rational system of first order difference equations in the plane with four parameters such that all fractions have a common denominator. We study, for the different values of the parameters, the global and local properties of…
We study a fractional reaction-diffusion system with two types of variables: activator and inhibitor. The interactions between components are modeled by cubical nonlinearity. Linearization of the system around the homogeneous state provides…
In this chapter we provide an introduction to fractional dissipative partial differential equations (PDEs) with a focus on trying to understand their dynamics. The class of PDEs we focus on are reaction-diffusion equations but we also…
No mixed research of hybrid and fractional-order systems into a cohesive and multifaceted whole can be found in the literature. This paper focuses on such a synergistic approach of the theories of both branches, which is believed to give…
Simple form scalar differential equation with delay and nonlinear negative periodic feedback is considered. The existence of several types of slowly oscillating periodic solutions is shown with the same and double periods of the feedback…
We derive and analyze a fully computable discrete scheme for fractional partial differential equations posed on the full space $\mathbb{R}^d$ . Based on a reformulation using the well-known Caffarelli-Silvestre extension, we study a…
This paper reviews a class of univariate piecewise polynomial functions known as discrete splines, which share properties analogous to the better-known class of spline functions, but where continuity in derivatives is replaced by (a…
The stochastic Cahn-Hilliard equation driven by a fractional Brownian sheet provides a more accurate model for correlated space-time random perturbations. This study delves into two key aspects: first, it rigorously examines the regularity…
The existence of positive solutions to the system of ordinary differential equations related to the Belousov-Zhabotinsky reaction is established. The key idea is to use successive approximation of solutions, ensuring its positivity. To…
We describe a general operational method that can be used in the analysis of fractional initial and boundary value problems with additional analytic conditions. As an example, we derive analytic solutions of some fractional generalisation…