Overview of One-Dimensional Continuous Functions with Fractional Integral and Applications in Reinforcement Learning

Keywords

Bounded variation, Variation (astronomy), Bounded function, Mathematics, Curse of dimensionality

References

• The relationship between the Box dimension of the Besicovitch functions and the orders of their fractional calculusYongshun Liang, Wei Su — 2008
• Fractional differentiability of nowhere differentiable functions and dimensions.Kiran M. Kolwankar, Anil D. Gangal — 1996
• Box dimension and fractional integral of linear fractal interpolation functionsHuo-Jun Ruan, Weiyi Su, Kui Yao — 2009
• Fractal dimensions of fractional integral of continuous functionsYongshun Liang — 2017
• Box dimensions of Riemann–Liouville fractional integrals of continuous functions of bounded variationYongshun Liang — 2010
• Nonlinear differential equations with marchaud‐hadamard‐type fractional derivative in the weighted space of summable functionsAnatoly A. Kilbas, Anatoly Titioura — 2007
• A physically based connection between fractional calculus and fractal geometrySalvatore Butera, Mario Di Paola — 2014
• On a class of fractal functions with graph Box dimension 2Tao Xie, S. P. Zhou — 2004
• Geometric and Physical Interpretation of Fractional Integration and Fractional DifferentiationIgor Podlubný — 2001
• Fractional Calculus: Quo Vadimus? (Where are we Going?)J. A. Tenreiro Machado, Francesco Mainardi, Virginia Kiryakova — 2015
• Continuous Functions Without DerivativesK. A. Bush — 1952
• Fractional Integrals and Derivatives to a Class of FunctionsQiang Xu — 2006
• Mastering the game of Go without human knowledgeDavid Silver, Julian Schrittwieser, Karen Simonyan — 2017
• A note on Katugampola fractional calculus and fractal dimensionsSaurabh Verma, P. Viswanathan — 2018
• Robust Multi-Agent Reinforcement Learning via Minimax Deep Deterministic Policy GradientShihui Li, Yi Wu, Xinyue Cui — 2019
• Fractal dimension of Riemann-Liouville fractional integral of 1-dimensional continuous functionsYong Shun Liang — 2018
• A review of definitions of fractional derivatives and other operatorsGrazielle Sales Teodoro, J. A. Tenreiro Machado, E. Capelas de Oliveira — 2019
• A High-Performance Stochastic Fractal Search Algorithm for Optimal Generation Dispatch ProblemLy Huu Pham, Minh Quan Duong, Van-Duc Phan — 2019
• Bivariate functions of bounded variation: Fractal dimension and fractional integralSaurabh Verma, P. Viswanathan — 2019
• Box Dimension of Weyl Fractional Integral of Continuous Functions with Bounded VariationLiru Mu, K. Yao, Y. S. Liang null — 2016

Cited by

• Influence of the Fractal Distribution of Particle Size on the Critical State Characteristics of Calcareous SandXue Shen, Yang Shen, Junhong Xu — 2022
• Design of intelligent hybrid NAR-GRNN paradigm for fractional order VDP chaotic system in cardiac pacemaker with relaxation oscillatorAyaz Hussain Bukhari, Muhammad Asif Zahoor Raja, Hani Alquhayz — 2023
• On a class of non-integer dimensional continuous functions with one unbounded variation pointPei-Zhi Liu, Yongshun Liang, Junru Wu — 2024

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