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Fractal and Fractional, Volume 8, Issue 11

November 2024 - 63 articles

Cover Story: Recently, a first-order recurrent neural network activated by a Morlet wavelet function was introduced which can identify multiple chaotic systems in a black-box scheme, i.e., the neural network knows nothing about the system to be identified and its structure and synaptic weights remain fixed. As a limitation, it was found that traditional systems such as Lorenz and Rösser were not identified, which raised the question: can such a first-order recurrent neural network improve its identification capabilities when modeled by fractional-order operators? The results suggest that such a combination does not cause significant changes in the identification properties of the neural network. However, scenarios were found where the neural algorithm identifies the Rössler system. View this paper
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Articles (63)

  • Article
  • Open Access
3 Citations
1,920 Views
17 Pages

DGGNets: Deep Gradient-Guidance Networks for Speckle Noise Reduction

  • Li Wang,
  • Jinkai Li,
  • Yi-Fei Pu,
  • Hao Yin and
  • Paul Liu

Speckle noise is a granular interference that degrades image quality in coherent imaging systems, including underwater sonar, Synthetic Aperture Radar (SAR), and medical ultrasound. This study aims to enhance speckle noise reduction through advanced...

  • Article
  • Open Access
12 Citations
1,593 Views
24 Pages

We show how a rescaling of fractional operators with bounded kernels may help circumvent their documented deficiencies, for example, the inconsistency at zero or the lack of inverse integral operator. On the other hand, we build a novel class of line...

  • Article
  • Open Access
1,197 Views
18 Pages

Due to increasing demands on the available railway infrastructure, accurate estimates of safety-critical track condition as well as breakdowns of individual track components are crucial. This task can be supported by analyzing track measurement data....

  • Article
  • Open Access
5 Citations
1,619 Views
21 Pages

A Computational Method for Solving Nonlinear Fractional Integral Equations

  • Rajaa T. Matoog,
  • Amr M. S. Mahdy,
  • Mohamed A. Abdou and
  • Doaa Sh. Mohamed

This article solves the nonlinear fractional integral equation (NFrIE) using the Genocchi polynomial method (GPM). We have provided proof to demonstrate the existence of a unique solution to the second sort of NFrIE in Hilbert space. The proof of the...

  • Article
  • Open Access
2 Citations
1,490 Views
23 Pages

In this work, the practical prescribed performance tracking issue for a class of fractional-order nonlinear multiple-input multiple-output (MIMO) systems with asymmetric full-state constraints and unmeasurable system states is investigated. A neural...

  • Article
  • Open Access
2,550 Views
27 Pages

Fractals as Pre-Training Datasets for Anomaly Detection and Localization

  • Cynthia I. Ugwu,
  • Emanuele Caruso and
  • Oswald Lanz

Anomaly detection is crucial in large-scale industrial manufacturing as it helps to detect and localize defective parts. Pre-training feature extractors on large-scale datasets is a popular approach for this task. Stringent data security, privacy reg...

  • Article
  • Open Access
1,221 Views
15 Pages

In this paper, the stability and l∞-gain problem are investigated for the Nabla discrete fractional linear positive systems with bounded time-varying delays. First, a sufficient condition and a necessary condition are presented to ensure the sy...

  • Article
  • Open Access
3 Citations
1,210 Views
19 Pages

In this paper, we present the existence of a mild solution for a class of a neutral stochastic integro-differential system over a Hilbert space. Such systems are influenced by both multiplicative and fractional noise, alongside non-instantaneous impu...

  • Article
  • Open Access
1,302 Views
19 Pages

In this paper, we will introduce a compact alternating direction implicit (ADI) difference scheme for solving the two-dimensional (2D) time fractional nonlinear Schrödinger equation. The difference scheme is constructed by using the L1−2&m...

  • Article
  • Open Access
1 Citations
1,712 Views
22 Pages

Multifractal Methods in Characterizing Pore Structure Heterogeneity During Hydrous Pyrolysis of Lacustrine Shale

  • Xiaofei Liang,
  • Qinhong Hu,
  • Xiugang Pu,
  • Wei Li,
  • Qiming Wang,
  • Mengdi Sun and
  • Wenzhong Han

By using gas physisorption and multifractal theory, this study analyzes pore structure heterogeneity and influencing factors during thermal maturation of naturally immature but artificially matured shale from the Kongdian Formation after being subjec...

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Fractal Fract. - ISSN 2504-3110