Related papers: Synchronization and secure communication using som…
We study a linear-quadratic optimal control problem involving a parabolic equation with fractional diffusion and Caputo fractional time derivative of orders $s \in (0,1)$ and $\gamma \in (0,1]$, respectively. The spatial fractional…
The aim of this study is to prove analytically that synchronization of a piece-wise continuous class of systems of fractional order can be achieved. Based on our knowledge, there are no numerical methods to integrate differential equations…
This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach…
We study the synchronization of chaotic units connected through time-delayed fluctuating interactions. We focus on small-world networks of Bernoulli and Logistic units with a fixed chiral backbone. Comparing the synchronization properties…
A semilinear initial-boundary value problem with a Caputo time derivative of fractional order $\alpha\in(0,1)$ is considered, solutions of which typically exhibit a singular behaviour at an initial time. For L1-type discretizations of this…
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…
For terminal value problems of fractional differential equations of order $\alpha \in (0,1)$ that use Caputo derivatives, shooting methods are a well developed and investigated approach. Based on recently established analytic properties of…
In this paper we investigate the dynamical behavior of fractional differential system associated to 5D Maxwell-Bloch model in terms of fractional Caputo derivatives.
Two replicas of spatially extended chaotic systems synchronize to a common spatio-temporal chaotic state when coupled above a critical strength. As a prototype of each single spatio-temporal chaotic system a lattice of maps interacting via…
In recent years, the use of variable-order differential operators has emerged as a powerful tool in the analysis of nonlinear fractional differential equations and chaotic systems. In finance, the accurate prediction of market trends and…
We introduce an efficient variational hybrid quantum-classical algorithm designed for solving Caputo time-fractional partial differential equations. Our method employs an iterable cost function incorporating a linear combination of overlap…
In this paper invariant subspace method has been employed for solving linear and non-linear fractional partial differential equations involving Caputo derivative. A variety of illustrative examples are solved to demonstrate the…
In this paper, we analyze disjoint distributionally chaotic abstract non-degenerate partial differential equations in Fr\' echet spaces, with integer or Caputo time-fractional derivatives. We present several illustrative examples and…
In this letter we consider a prototype model which is described as an autonomous continuous time delayed differential equation with just one variable. The chaos has been investigated with variable delay time and the synchronization…
Fractional derivative and delay are important tools in modeling memory properties in the natural system. This work deals with the stability analysis of a fractional order delay differential equation \begin{equation*} D^\alpha x(t)=\delta…
The linear response of synchronized time-delayed chaotic systems to small external perturbations, i.e., the phenomenon of chaos pass filter, is investigated for iterated maps. The distribution of distances, i.e., the deviations between two…
In this paper the chaos control in the discrete logistic map of fractional order is obtained with an impulsive control algorithm. The underlying discrete initial value problem of fractional order is considered in terms of Caputo delta…
In this work, the synchronization problem of a master-slave system of autonomous ordinary differential equations (ODEs) is considered. Here, the systems are, chaotic with a nonlinearity represented by a piecewise linear function,…
In this paper, a chaos control algorithm for a class of piece-wise continuous chaotic systems of fractional order, in the Caputo sense, is proposed. With the aid of Filippov's convex regularization and via differential inclusions, the…
In this chapter, we mainly review theoretical results on inverse source problems for diffusion equations with the Caputo time-fractional derivatives of order $\alpha\in(0,1)$. Our survey covers the following types of inverse problems: 1.…