In this paper, we consider fractional parabolic equation of the form ∂u ∂t = −(−∆) α 2 u+ uẆ (t, x), where −(−∆)α2 with α ∈ (0, 2] is a fractional Laplacian and Ẇ is a Gaussian noise colored in space and time. The precise moment Lyapunov exponents for the Stratonovich solution and the Skorohod solution are obtained by using a variational inequality and a Feynman-Kac type large deviation result ...

This paper studies an LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties. The delay is assumed to be time-varying and belong to a given interval, which means that lower and upper bounds of this interval time-varying delay are available. The uncertainty under consideration includes polytopic-type uncerta...

This paper is presented on the theory and applications of fractional-order chaotic system described by Caputo fractional derivative. Considering new model, it important to establish presence or absence behaviors. The Lyapunov exponents in context will be our fundamental tool arrive at conclusions. variations model’s parameters generate behavior, general, which established using bifurcation diag...

This study investigates the multistability phenomenon and coexisting attractors in modified Autonomous Van der Pol-Duffing (MAVPD) system its fractional-order form. The analytical conditions for existence of periodic solutions integer-order via Hopf bifurcation are discussed. In addition, approximating fractional version to obtained theory systems. Moreover, technique hidden localization MAVPD ...

In this paper, we consider controlling a class of single-input-single-output (SISO) commensurate fractional-order nonlinear systems with parametric uncertainty and external disturbance. Based on backstepping approach, an adaptive controller is proposed laws that are used to estimate the unknown system parameters bound Instead using discontinuous functions such as $\mathrm{sign}$ function, auxil...

The ideal magnetic flux-controlled memristor was introduced into a four-dimensional chaotic system and combined with fractional calculus theory, novel commensurate fractional-order proposed solved using the Adomian decomposition method. orders, parameters, initial values were studied as independent variables in bifurcation diagram Lyapunov exponents spectrum, it discovered that changing these c...

Based on a quantum logistic map and Caputo-like delta difference operator, fractional-order improved map, which has hidden attractors, was constructed. Its dynamical behaviors are investigated by employing phase portraits, bifurcation diagrams, Lyapunov spectra, mapping, 0-1 testing. It is shown that the proposed influenced both parameters fractional order. Then, complexity of explored through ...

Abstract In this paper, we consider a new fractional-order predator–prey model with Holling type-III functional response and stage structure. Based on the Lyapunov stability theory by constructing suitable functional, obtain some sufficient conditions for existence uniqueness of positive solutions asymptotic equilibrium to system. Finally, give numerical examples illustrate feasibility our resu...

This paper investigates the switching-jumps-dependent quasi-synchronization issue for fractional-order memristive neural networks (FMNNs). First, a simplied linear feedback controller is applied. Then, in terms of several fractional order differential inequalities and two kinds Lyapunov functions, criteria expressed by matrix inequality (LMI)-based form algebraic are established, respectively. ...