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Fractional differential equations of Caputo–Katugampola type and numerical solutions

Author

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  • Zeng, Shengda
  • Baleanu, Dumitru
  • Bai, Yunru
  • Wu, Guocheng

Abstract

This paper is concerned with a numerical method for solving generalized fractional differential equation of Caputo–Katugampola derivative. A corresponding discretization technique is proposed. Numerical solutions are obtained and convergence of numerical formulae is discussed. The convergence speed arrives at O(ΔT1−α). Numerical examples are given to test the accuracy.

Suggested Citation

  • Zeng, Shengda & Baleanu, Dumitru & Bai, Yunru & Wu, Guocheng, 2017. "Fractional differential equations of Caputo–Katugampola type and numerical solutions," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 549-554.
    • Handle: RePEc:eee:apmaco:v:315:y:2017:i:c:p:549-554
    DOI: 10.1016/j.amc.2017.07.003
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    References listed on IDEAS

    as
    1. Katugampola, Udita N., 2015. "Mellin transforms of generalized fractional integrals and derivatives," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 566-580.
    2. Wu, Guo-Cheng & Baleanu, Dumitru & Deng, Zhen-Guo & Zeng, Sheng-Da, 2015. "Lattice fractional diffusion equation in terms of a Riesz–Caputo difference," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 335-339.
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    Cited by:

    1. Cai, Ruiyang & Ge, Fudong & Chen, YangQuan & Kou, Chunhai, 2019. "Regional observability for Hadamard-Caputo time fractional distributed parameter systems," Applied Mathematics and Computation, Elsevier, vol. 360(C), pages 190-202.
    2. Wang, Zhe & Xue, Dingyu & Pan, Feng, 2021. "Observer-based robust control for singular switched fractional order systems subject to actuator saturation," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    3. Zhang, Tao & Lu, Zhong-rong & Liu, Ji-ke & Chen, Yan-mao & Liu, Guang, 2023. "Parameter estimation of linear fractional-order system from laplace domain data," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    4. Kadak, Ugur, 2022. "Max-product type multivariate sampling operators and applications to image processing," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    5. Verma, S. & Viswanathan, P., 2018. "A note on Katugampola fractional calculus and fractal dimensions," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 220-230.
    6. Sivalingam, S M & Kumar, Pushpendra & Trinh, Hieu & Govindaraj, V., 2024. "A novel L1-Predictor-Corrector method for the numerical solution of the generalized-Caputo type fractional differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 462-480.

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