Delay-Independent Stability of Riemann–Liouville Fractional Neutral-Type Delayed Neural Networks

Existence and Globally Asymptotic Stability of Equilibrium Solution for Fractional-Order Hybrid BAM Neural Networks with Distributed Delays and Impulses

“…Different from fractional Lyapunov functional method in [30,32,37], an appropriate Lyapunov functional composed of fractional integral and definite integral terms in the proof of Theorem 11 is presented, and we only Complexity need to calculate its first-order derivative to derive stability conditions. As discussed in [35], in general speaking, it is very difficult to calculate the fractional-order derivatives of a Lyapunov functional. The main advantage of our constructed method is that we can avoid computing the fractional-order derivatives of the Lyapunov functional.…”

“…For example, Song and Cao [26] have established some sufficient conditions to 2 Complexity ensure the existence and uniqueness of the nontrivial solution by using the contraction mapping principle, Krasnoselskii fixed point theorem, and the inequality technique, in which uniform stability conditions of fractional-order neural networks are also derived in fixed time-intervals. Note that timedelay (see [23][24][25][31][32][33][34][35][36][37]) is a common phenomenon and is inevitable in practice, which often exists in almost every neural network and has an important effect on the stability and performance of system.…”

“…The finite-time stability of Caputo fractional-order delayed neural networks has been studied by applying Gronwall's inequality approach and inequality scaling techniques [33,34]. The delay-independent stability criteria of Riemann-Liouville fractional-order neutral-type delayed neural networks have been proposed based on classical Lyapunov functional method [35]. The uniform stability and global stability of fractional neural networks with delay are considered based on the fractional calculus theory and analytical techniques [36].…”

Projective synchronization of fractional-order delayed neural networks based on the comparison principle

“…Compared to classical integer-order models, fractional-order calculus offers an excellent instrument for the description of memory and hereditary properties of dynamical processes. The existence of infinite memory can help fractional-order models better describe the system's dynamical behaviors as illustrated in [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Taking these factors into consideration, fractional calculus was introduced to neural networks forming fractional-order neural networks, and some interesting results on synchronization were demonstrated [24][25][26][27][28][29].…”

Periodic solutions for complex-valued neural networks of neutral type by combining graph theory with coincidence degree theory

“…On the other hand, time delays have been extensively studied in last decades due to their potential existence in many fields [12,13,[18][19][20]. Up to now, the dynamical behaviors of neural networks of neutral type have been extensively investigated and a lot of interesting results on the global asymptotic stability and global exponential stability of equilibrium point and periodic solutions for neural networks of neutral type have been published, for example, see [18,[21][22][23][24][25][26][27][28] and the references therein.…”