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Fractal and Fractional, Volume 8, Issue 9

September 2024 - 54 articles

Cover Story: Neural fractional differential equations (FDEs) are a neural network architecture designed to fit the solutions of fractional differential equations to data. This architecture combines an analytical component, the fractional derivative, with a neural network component, forming an initial value problem. We investigate the non-uniqueness of the optimal order of the derivative and its interaction with the neural network. We examine how different initialisations and values of the order of the derivative (in the optimisation process) impact its final optimal value. Consequently, neural FDEs do not require a unique α value; instead, they can use a wide range of α values to fit data. This flexibility is beneficial when fitting to given data is required and the underlying physics is not known. View this paper
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Articles (54)

  • Article
  • Open Access
4 Citations
1,833 Views
16 Pages

Ultrasound imaging is widely used in medical diagnostics due to its non-invasive and real-time capabilities. However, existing methods often overlook the benefits of fractional-order filters for denoising and dehazing. Thus, this work introduces an e...

  • Article
  • Open Access
25 Citations
1,491 Views
22 Pages

In this study, a model-free  PIφ-sliding mode control ( PIφ-SMC) methodology is proposed to synchronize a specific class of chaotic fractional-order memristive neural network systems (FOMNNSs) with delays and input saturation. The fracti...

  • Article
  • Open Access
3 Citations
1,041 Views
16 Pages

This paper derives the sharp bounds for Hermite–Hadamard inequalities in the context of Riemann–Liouville fractional integrals. A generalization of Jensen’s inequality called the Jensen–Mercer inequality is used for general po...

  • Article
  • Open Access
1,298 Views
15 Pages

The ultrasonic vibration rock-breaking method has been successfully applied to hard rock due to its high efficiency and controllable energy, providing a novel approach for the development of a more efficient, intelligent, safe, and environmentally fr...

  • Article
  • Open Access
3 Citations
1,767 Views
22 Pages

Event-triggering mechanisms reported in the existing prescribed-time (PT) control do not adequately capture the dynamic nature of network environments, and are not applied to distributed consensus tracking problems with unknown time delays. Therefore...

  • Article
  • Open Access
1 Citations
1,441 Views
23 Pages

A Novel Fractal Model for Contact Resistance Based on Axisymmetric Sinusoidal Asperity

  • Yue Liu,
  • Shihao Yang,
  • Weikun Wang,
  • Shuai Wang,
  • Qi An,
  • Min Huang and
  • Shuangfu Suo

In this paper, a novel fractal model for the contact resistance based on axisymmetric sinusoidal asperity is proposed, which focuses on the resistance characteristics of the rough interface at a microscopic scale. By introducing the unique geometric...

  • Article
  • Open Access
4 Citations
973 Views
27 Pages

We explore the existence, uniqueness, and multiplicity of positive solutions to a system of Hadamard fractional differential equations that contain fractional integral terms. Defined on a finite interval, this system is subject to general coupled non...

  • Article
  • Open Access
3 Citations
924 Views
14 Pages

Modelling Yeast Prion Dynamics: A Fractional Order Approach with Predictor–Corrector Algorithm

  • Daasara Keshavamurthy Archana,
  • Doddabhadrappla Gowda Prakasha and
  • Nasser Bin Turki

This work aims to comprehend the dynamics of neurodegenerative disease using a mathematical model of fractional-order yeast prions. In the context of the Caputo fractional derivative, we here study and examine the solution of this model using the Pre...

  • Article
  • Open Access
3 Citations
1,075 Views
24 Pages

In this article, we develop multiplicative fractional versions of Simpson’s and Newton’s formula-type inequalities for differentiable generalized convex functions with the help of established identities. The main motivation for using gene...

  • Article
  • Open Access
2 Citations
1,857 Views
24 Pages

The study investigates the nonlinear contagion, tail dependence, and Granger causality relations with TAR-TR-GARCH–copula causality methods for daily Bitcoin, Fintech, energy consumption, and CO2 emissions in addition to examining these series...

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Fractal Fract. - ISSN 2504-3110Creative Common CC BY license