This paper discusses the quasi-uniform synchronization issue for fractional-orderneural networks (FONNs) with leakage and discrete delays. The impacts of leakage delay, discrete delay and fractional derivative on the quasi-uniform synchronization are simultaneously considered. By employing the Laplace transformation, the Gronwall inequality and analytical techniques, several sufficient criteria of the quasi-uniform synchronization for FONNs with leakage and discrete delays are established. The criterion conditions reveal the less conservatism because the order of fractional derivative is in the interval (0,2). The presented results are related to the classical exponential function, where it is not necessary to calculate fractional-order derivatives to reduce the complexities. Taking into account the different orders of fractional derivative, the validity and applicability of the proposed results are verified by the numerical simulations.

Quasi-uniform synchronization of Caputo type fractional neural networks with leakage and discrete delays★

Hybrid control design for Mittag-Leffler projective synchronization on FOQVNNs with multiple mixed delays and impulsive effects

This paper is devoted to discussing the globally projective synchronization of Caputo fractional-order quaternion-valued neural networks (FOQVNNs) with discrete and distributed delays. Without decomposing the FOQVNNs into several subsystems, by employing the Lyapunov direct method and inequality techniques, the algebraic criterion for the globally projective synchronization is derived. The effectiveness of the proposed result is illustrated by the MATLAB toolboxes and numerical simulation.

Globally projective synchronization for Caputo fractional quaternion-valued neural networks with discrete and distributed delays


 The appreciation of inequalities in convexity is critical for fractional calculus and its application in a variety of fields. In this paper, we provide a unique analysis based on Hermite-Hadamard inequalities in the context of newly defined class of convexity which is known as left and right harmonically $ {h} $-convex IVF (left and right $ \mathcal{H}$-$ {h} $-convex IVF), as well as associated integral and fractional inequalities, are addressed by the suggested technique. Because of its intriguing character in the numerical sciences, there is a strong link between fractional operators and convexity. There have also been several exceptional circumstances studied, and numerous well-known Hermite-Hadamard inequalities have been derived for left and right $ \mathcal{H}$-$ {h} $-convex IVF. Moreover, some applications are also presented in terms of special cases which are discussed in this study. The plan's outcomes demonstrate that the approach may be implemented immediately and is computationally simple and precise. We believe, our findings, generalize certain well-known new and classical harmonically convexity discoveries from the literature.


New class of convex interval-valued functions and Riemann Liouville fractional integral inequalities

This paper is devoted to the exploration of the global asymptotic synchronization (GAS) and global Mittag–Leffler synchronization (GMLS) issues on bidirectional associative memory reaction-diffusion neural networks (BAMRDNNs), which include a Caputo’s fractional partial differential operator , leakage and discrete delays. By means of the Green’s theorem, Jensen’s integral inequality and Lyapunov functional approach, several synchronization criteria are established by using the hybrid controllers . The presented results are described in the algebraic inequalities form, which can immensely reduce the computational complexity. Moreover, these results reveal the impact of the network system coefficient matrices on GAS and GMLS. Finally, in the three-dimensional space, the effectiveness and practicability of these synchronization criteria are confirmed by choosing different derivative orders and diffusion coefficients . 

Global synchronization for BAM delayed reaction-diffusion neural networks with fractional partial differential operator

This paper talks about the global synchronization of delayed fractional-order complex valued neural networks (FOCVNNs) with leakage delay. A new fractional differential inequality is proposed, which offers an important tool in the investigation of synchronization about FOCVNNs. Through constructing appropriate Lyapunov function and using the fractional order comparison theory, some new synchronization conditions are established. A numerical example is given to demonstrate the feasibility of the proposed method.

Synchronization of delayed fractional-order complex-valued neural networks with leakage delay

This paper focuses on investigating the finite-time projective synchronization of Caputo type fractional-order complex-valued neural networks with time delay (FOCVNNTD). Based on the properties of fractional calculus and various inequality techniques, by constructing suitable the Lyapunov function and designing two new types controllers, i.e., feedback controller and adaptive controller, two sufficient criteria are derived to ensure the projective finite-time synchronization between drive and response systems, and the synchronization time can effectively be estimated. Finally, two numerical examples are presented to verify the effectiveness and feasibility of the proposed results.

Hongmei Zhang

Papers

Quasi-uniform synchronization of Caputo type fractional neural networks with leakage and discrete delays★

Hybrid control design for Mittag-Leffler projective synchronization on FOQVNNs with multiple mixed delays and impulsive effects

Synchronization of delayed fractional-order complex-valued neural networks with leakage delay

Globally projective synchronization for Caputo fractional quaternion-valued neural networks with discrete and distributed delays

Finite-Time Projective Synchronization of Caputo Type Fractional Complex-Valued Delayed Neural Networks