Asymptotical Stability of Riemann–Liouville Fractional-Order Neutral-Type Delayed Projective Neural Networks

Li, Jindong; Wu, Zeng-bao; Huang, Nan-jing

doi:10.1007/s11063-019-10050-8

Cited by 20 publications

(9 citation statements)

References 31 publications

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“…. , and according to Remark 5 the zero vector is an equilibrium of RINN (15). Therefore, if we know the equilibrium point x * ∈ R n of (9), then we can construct a model with zero equilibrium point.…”

Section: Equilibrium Of Rl Fractional Model With Random Impulsesmentioning

confidence: 99%

“…. Use (16) to obtain the fractional Dini derivative of V along the trajectories of solutions of RINN (15):…”

Section: Definition 6 Letmentioning

confidence: 99%

“…Let x 0 ∈ R n be an arbitrary initial value and the stochastic process x(t; x 0 , {τ k }) be a solution of the initial value problem for RINN (9). Then the stochastic process y(t; x 0x * , {τ k }) is a solution of the initial value problem for RINN (15).…”

Section: Consider the Lyapunov Functionmentioning

confidence: 99%

“…Note that the case of fractional-neural networks with Riemann-Liouville (RL) fractional derivatives is not well studied because of this type of derivative and the required initial condition (see, for example, [10,11,15,27,29]). At the same time, there are some inaccuracies when the RL fractional derivative is applied.…”

Section: Introductionmentioning

confidence: 99%

“…At the same time, there are some inaccuracies when the RL fractional derivative is applied. For example, in papers [10,15,27] the RL fractional integral and the RL fractional derivative, respectively, are not well defined in the initial conditions associated with the RL fractional model with delay. In [30] the equilibrium point is defined by an equation which has only the zero solution (see Remarks 3 and 1).…”

Section: Introductionmentioning

confidence: 99%

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Mean-square stability of Riemann–Liouville fractional Hopfield’s graded response neural networks with random impulses

et al. 2021

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In this paper a model of Hopfield’s graded response neural network is investigated. A network whose neurons are subject to a certain impulsive state displacement at random times is considered. The model is set up and studied. The presence of random moments of impulses in the model leads to a change of the solutions to stochastic processes. Also, we use the Riemann–Liouville fractional derivative to model adequately the long-term memory and the nonlocality in the neural networks. We set up in an appropriate way both the initial conditions and the impulsive conditions at random moments. The application of the Riemann–Liouville fractional derivative leads to a new definition of the equilibrium point. We define mean-square Mittag-Leffler stability in time of the equilibrium point of the model and study this type of stability. Some sufficient conditions for this type of stability are obtained. The general case with time varying self-regulating parameters of all units and time varying functions of the connection between two neurons is studied.

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Section: Equilibrium Of Rl Fractional Model With Random Impulsesmentioning

confidence: 99%

“…. Use (16) to obtain the fractional Dini derivative of V along the trajectories of solutions of RINN (15):…”

Section: Definition 6 Letmentioning

confidence: 99%

Section: Consider the Lyapunov Functionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Mean-square stability of Riemann–Liouville fractional Hopfield’s graded response neural networks with random impulses

et al. 2021

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Qualitative analysis of solutions of obstacle elliptic inclusion problem with fractional Laplacian

Zeng

Cen

Atangana

et al. 2021

Z. Angew. Math. Phys.

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In this paper, we study an elliptic obstacle problem with a generalized fractional Laplacian and a multivalued operator which is described by a generalized gradient. Under quite general assumptions on the data, we employ a surjectivity theorem for multivalued mappings generated by the sum of a maximal monotone multivalued operator and a bounded multivalued pseudomonotone mapping to prove that the set of weak solutions to the problem is nonempty, bounded and closed. Then, we introduce a sequence of penalized problems without obstacle constraints. Finally, we prove that the Kuratowski upper limit of the sets of solutions to penalized problems is nonempty and is contained in the set of solutions to original elliptic obstacle problem, i.e., ∅ ≠ wlim sup n→∞ Sn = slim sup n→∞ Sn ⊂ S.

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Passivity Analysis of Fractional-Order Neural Networks with Time-Varying Delay Based on LMI Approach

Thuận

Huyền

2020

Circuits Syst Signal Process

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Asymptotical Stability of Riemann–Liouville Fractional-Order Neutral-Type Delayed Projective Neural Networks

Cited by 20 publications

References 31 publications

Mean-square stability of Riemann–Liouville fractional Hopfield’s graded response neural networks with random impulses

Mean-square stability of Riemann–Liouville fractional Hopfield’s graded response neural networks with random impulses

Qualitative analysis of solutions of obstacle elliptic inclusion problem with fractional Laplacian

Passivity Analysis of Fractional-Order Neural Networks with Time-Varying Delay Based on LMI Approach

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