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International Journal of Control Volume 90, 2017 - Issue 6: Applied Fractional calculus in Modelling, Analysis and Design of Control Systems
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Original Articles

Numerical algorithms for Caputo fractional-order differential equations

Dingyü XueSchool of Information Science and Engineering, Northeastern University, Shenyang, P. R. ChinaCorrespondence[email protected]
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Lu BaiSchool of Information Science and Engineering, Northeastern University, Shenyang, P. R. China;School of Information Engineering, Shenyang University, Shenyang, P. R. ChinaView further author information
Pages 1201-1211 | Received 28 Jun 2015, Accepted 22 Feb 2016, Published online: 23 Mar 2016

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Yuman Li, Yiheng Wei, Chen Yuquan & Yong Wang. (2021) H∞ bounded real lemma for singular fractional-order systems. International Journal of Systems Science 52:12, pages 2538-2548.
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Yan Liu, Yunzhou Zhang, Shangdong Zhu, Lei Wang & Le Zhou. (2020) Dynamical behaviour of stochastic competition system with harvest and Lévy jumps. Journal of Control and Decision 7:4, pages 309-326.
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Articles from other publishers (16)

Ke-Qiang Zhang, Xue-Jun Cao & Yu-Lan Wang. (2022) A high-precision numerical method to simulating the fractional-order EI Ni ñ o chaotic systems with Riemann–Liouville fractional derivative . Journal of Low Frequency Noise, Vibration and Active Control 42:1, pages 134-145.
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Dandan Dai, Xiaoyu Li, Zhiyuan Li, Wei Zhang & Yulan Wang. (2023) Numerical Simulation of the Fractional-Order Lorenz Chaotic Systems with燙aputo Fractional Derivative. Computer Modeling in Engineering & Sciences 135:2, pages 1371-1392.
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XIAOYU LI & YU-LAN WANG. (2022) NUMERICAL SIMULATION OF THE FRACTIONAL-ORDER RÖSSLER CHAOTIC SYSTEMS WITH GRÜNWALD–LETNIKOV FRACTIONAL DERIVATIVE. Fractals 30:08.
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Lu Bai & Dingyu Xue. (2022) Block Diagram Modeling and Simulation for Delay Fractional-Order Differential Equation. Block Diagram Modeling and Simulation for Delay Fractional-Order Differential Equation.
Lu Bai & Dingyü Xue. (2022) Numerical Algorithm for Calculating the Time Domain Response of Fractional Order Transfer Function. Fractal and Fractional 6:2, pages 122.
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Yunfan Yang, Liang Ling, Tao Zhang, Kaiyun Wang & Wanming Zhai. (2021) An Advanced Antislip Control Algorithm for Locomotives Under Complex Friction Conditions. Journal of Computational and Nonlinear Dynamics 16:10.
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Yang Yang & Xiuqin Wang. (2020) A Class of Time-delay Model Calculation for Grey System Modeling and Analysis. A Class of Time-delay Model Calculation for Grey System Modeling and Analysis.
Zhiyao Ma & Hongjun Ma. (2020) Adaptive Fuzzy Backstepping Dynamic Surface Control of Strict-Feedback Fractional-Order Uncertain Nonlinear Systems. IEEE Transactions on Fuzzy Systems 28:1, pages 122-133.
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Jianhua Guo, Weilun Liu, Liang Chu & Jingyuan Zhao. (2019) Fractional-Order Modeling and Parameter Identification for Ultracapacitors with a New Hybrid SOA Method. Energies 12:22, pages 4251.
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Yi Yang & Haiyan Henry Zhang. (2019) Fractional Calculus with its Applications in Engineering and Technology. Synthesis Lectures on Mechanical Engineering 3:1, pages 1-107.
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Yanting Zhao, Yiheng Wei, Yuquan Chen & Yong Wang. (2018) A New Look at the Fractional Initial Value Problem: The Aberration Phenomenon. Journal of Computational and Nonlinear Dynamics 13:12.
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Lu Bai & Dingyü Xue. (2018) Universal block diagram based modeling and simulation schemes for fractional-order control systems. ISA Transactions 82, pages 153-162.
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Yanting Zhao, Yiheng Wei, Jianmei Shuai & Yong Wang. (2018) Fitting of the initialization function of fractional order systems. Nonlinear Dynamics 93:3, pages 1589-1598.
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Dingyü Xue & Lu Bai. (2017) Benchmark problems for Caputo fractional-order ordinary differential equations. Fractional Calculus and Applied Analysis 20:5, pages 1305-1312.
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Leif Kari. (2017) Dynamic stiffness of chemically and physically ageing rubber vibration isolators in the audible frequency range. Continuum Mechanics and Thermodynamics 29:5, pages 1027-1046.
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Yanting Zhao, Yiheng Wei, Jiachang Wang & Yong Wang. (2018) The Simulation Technique for Fractional Order Systems with Nonzero Initial Value. SSRN Electronic Journal.
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