Journal ArticleDOI
Variable-order fractional discrete-time recurrent neural networks
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TLDR
Fractional discrete-time recurrent neural network is proposed on an isolated time scale and short memory and variable-order fractional neural networks are given according to the stability conditions.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 2020-05-15. It has received 97 citations till now. The article focuses on the topics: Fractional calculus & Recurrent neural network.read more
Citations
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Bifurcation Properties for Fractional Order Delayed BAM Neural Networks
TL;DR: In this article, the stability and Hopf bifurcation of fractional order BAM neural networks with or without leakage delay were investigated. And the authors derived the stability condition and the sufficient criterion of existence of Hopf-bifurcation for fractional-order BAM networks with delay (leakage delay).
Journal ArticleDOI
Short memory fractional differential equations for new memristor and neural network design
TL;DR: The new features of short memory fractional differential equations are used to improve the performance of networks and discussions are made about potential applications.
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New fractional variable-order creep model with short memory
TL;DR: A creep model is established by use of the short memory effect on each creep stage, and the efficiency of the model is verified.
Journal ArticleDOI
New fractional signal smoothing equations with short memory and variable order
TL;DR: In this paper, the effect of uncertainty in a diabetes model and its resulting complications is investigated as a practical application, and the superconvergent results on the graded mesh are studied.
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A novel color image encryption algorithm based on a fractional-order discrete chaotic neural network and DNA sequence operations
TL;DR: Experimental results and the security analysis show that the proposed algorithm has better performance than those reported in the literature and can resist typical attacks.
References
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Journal Article
Capacitor theory
S. Westerlund,L. Ekstam +1 more
TL;DR: In this article, a new linear capacitor model is proposed based on Curie's empirical law of 1889, which states that the current through a capacitor is i(t)=U/sub 0/(h/sub 1/t/sup n/), where h is the dc voltage applied at t = 0, and 0 > 0.
Journal ArticleDOI
Initial value problems in discrete fractional calculus
Ferhan M. Atıcı,Paul W. Eloe +1 more
TL;DR: In this article, the commutativity properties of the fractional sum and fractional difference operators are studied. But the particular goal is to define and solve well-defined discrete fractional differential equations.
Book
Discrete Fractional Calculus
TL;DR: In this article, the Discrete Delta Fractional Calculus and Laplace Transforms are used to solve boundary value problems in the Basic Difference Calculus (BDC) and Quantum Calculus on Mixed Time Scales.
Journal ArticleDOI
On Riemann and Caputo fractional differences
TL;DR: This paper defines left and right Caputo fractional sums and differences, study some of their properties and then relate them to Riemann-Liouville ones studied before by Miller K. S. and Ross B. and Atici F.M.