Fractional Derivative

Fractional derivatives extend the concept of derivatives to non-integer orders, enabling the modeling of systems with memory effects and long-range dependencies not captured by traditional integer-order models. Current research focuses on applying fractional derivatives within various machine learning frameworks, including physics-informed neural networks (PINNs), Kolmogorov-Arnold networks (KANs), and graph neural networks, often employing techniques like fractional gradient descent and operational matrices for efficient computation. These advancements are significantly impacting diverse fields, improving the accuracy and efficiency of solving fractional differential equations in areas such as signal processing, control systems, and image analysis, as well as enabling more robust modeling of complex physical phenomena.

Papers

November 30, 2023

Convergence Analysis of Fractional Gradient Descent
Ashwani Aggarwal
Gradient Descent Convergence Analysis Fractional Derivative Order Derivative Convergence Property Fractional Order Gradient

October 18, 2023

Fractional Concepts in Neural Networks: Enhancing Activation and Loss Functions
Zahra Alijani, Vojtech Molek
Neural Network Loss Function Targeted Activation Penalty Fractional Derivative Fractional Concept

October 7, 2023

September 23, 2023

Time-Series Forecasting: Unleashing Long-Term Dependencies with Fractionally Differenced Data
Sarit Maitra, Vivek Mishra, Srashti Dwivedi, Sukanya Kundu, Goutam Kumar Kundu
Time Series Data State of the Art Forecasting Fractional Derivative Integer Arithmetic Question Based Dependency Novel Forecasting

September 14, 2023

deepFDEnet: A Novel Neural Network Architecture for Solving Fractional Differential Equations
Ali Nosrati Firoozsalari, Hassan Dana Mazraeh, Alireza Afzal Aghaei, Kourosh Parand
Deep Neural Network Differential Equation Neural Network Architecture Fractional Derivative

August 30, 2023

A numerical approach for the fractional Laplacian via deep neural networks
Nicolás Valenzuela
Deep Neural Network Stochastic Gradient Descent Numerical Method Fractional Derivative Boundary Condition

April 3, 2023

Laplace-fPINNs: Laplace-based fractional physics-informed neural networks for solving forward and inverse problems of subdiffusion
Xiong-Bin Yan, Zhi-Qin John Xu, Zheng Ma
Inverse Problem Differential Equation Fractional Derivative Laplace fPINNs

March 13, 2023

Fractional dynamics foster deep learning of COPD stage prediction
Chenzhong Yin, Mihai Udrescu, Gaurav Gupta, Mingxi Cheng, Andrei Lihu, Lucretia Udrescu, Paul Bogdan, David M Mannino, Stefan Mihaicuta
Deep Learning Fractional Derivative Chronic Obstructive Pulmonary Disease Neural Fractional

January 20, 2023

Exploration of Various Fractional Order Derivatives in Parkinson's Disease Dysgraphia Analysis
Jan Mucha, Zoltan Galaz, Jiri Mekyska, Marcos Faundez-Zanuy, Vojtech Zvoncak, Zdenek Smekal, Lubos Brabenec, Irena Rektorova
Environment Exploration Parkinson Disease Fractional Derivative Handwriting Feature Handwriting Task Handwriting Dataset Disease Dysgraphia

November 24, 2022

Robust fractional-order fast terminal sliding mode control of aerial manipulator derived from a mutable inertia parameters model
Wenlei Zheng, Zhan Li, Bingkai Xiu, Bingliang Zhao, Zhigang Guo
Aerial Manipulator Fractional Derivative Sliding Mode Control Mode Switching Inertia Parameter

October 26, 2022

Adaptive deep density approximation for fractional Fokker-Planck equations
Li Zeng, Xiaoliang Wan, Tao Zhou
Fractional Derivative Fokker Planck Equation Neural Density Nonlocal Operator

September 30, 2022

The Role of Time Delay in Sim2real Transfer of Reinforcement Learning for Cyber-Physical Systems
Mohamad Chehadeh, Igor Boiko, Yahya Zweiri
Reinforcement Learning Integral Role Cyber Physical System Fractional Derivative Time Delay Sim2Real Transfer Markovian Sequence

May 1, 2022

Using a novel fractional-order gradient method for CNN back-propagation
Mundher Mohammed Taresh, Ningbo Zhu, Talal Ahmed Ali Ali, Mohammed Alghaili, Weihua Guo
Back Propagation Fractional Derivative Neural Fractional Fractional Order Gradient

April 10, 2022

Real order total variation with applications to the loss functions in learning schemes
Pan Liu, Xin Yang Lu, Kunlun He
Financial Application Loss Function Total Variation Fractional Derivative Calysto Scheme

November 12, 2021

Frequency learning for structured CNN filters with Gaussian fractional derivatives
Nikhil Saldanha, Silvia L. Pintea, Jan C. van Gemert, Nergis Tomen
Receptive Field High Frequency Fractional Derivative Classical Convolutional Neural Network

Fractional Derivative

Papers

Convergence Analysis of Fractional Gradient Descent

Fractional Concepts in Neural Networks: Enhancing Activation and Loss Functions

HNS: An Efficient Hermite Neural Solver for Solving Time-Fractional Partial Differential Equations

PMNN:Physical Model-driven Neural Network for solving time-fractional differential equations

Time-Series Forecasting: Unleashing Long-Term Dependencies with Fractionally Differenced Data

deepFDEnet: A Novel Neural Network Architecture for Solving Fractional Differential Equations

A numerical approach for the fractional Laplacian via deep neural networks

Laplace-fPINNs: Laplace-based fractional physics-informed neural networks for solving forward and inverse problems of subdiffusion

Fractional dynamics foster deep learning of COPD stage prediction

Exploration of Various Fractional Order Derivatives in Parkinson's Disease Dysgraphia Analysis

Robust fractional-order fast terminal sliding mode control of aerial manipulator derived from a mutable inertia parameters model

Adaptive deep density approximation for fractional Fokker-Planck equations

The Role of Time Delay in Sim2real Transfer of Reinforcement Learning for Cyber-Physical Systems

Using a novel fractional-order gradient method for CNN back-propagation

Real order total variation with applications to the loss functions in learning schemes

Frequency learning for structured CNN filters with Gaussian fractional derivatives