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Application of SubIval in solving initial value problems with fractional derivatives

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  • Sowa, Marcin

Abstract

The application of a numerical method for the approximation of the fractional derivative (in Riemann–Liouville and Caputo definitions) in initial value problems is discussed. The method (previously known as the subinterval-based method) is now referred to by its acronym, SubIval, for simpler future references.

Suggested Citation

  • Sowa, Marcin, 2018. "Application of SubIval in solving initial value problems with fractional derivatives," Applied Mathematics and Computation, Elsevier, vol. 319(C), pages 86-103.
    • Handle: RePEc:eee:apmaco:v:319:y:2018:i:c:p:86-103
    DOI: 10.1016/j.amc.2017.01.047
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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. Garrappa, Roberto, 2015. "Trapezoidal methods for fractional differential equations: Theoretical and computational aspects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 110(C), pages 96-112.
    3. Sierociuk, Dominik & Skovranek, Tomas & Macias, Michal & Podlubny, Igor & Petras, Ivo & Dzielinski, Andrzej & Ziubinski, Pawel, 2015. "Diffusion process modeling by using fractional-order models," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 2-11.
    4. Saeed, Umer & ur Rehman, Mujeeb, 2015. "Haar wavelet Picard method for fractional nonlinear partial differential equations," Applied Mathematics and Computation, Elsevier, vol. 264(C), pages 310-322.
    5. Luo, Wei-Hua & Huang, Ting-Zhu & Wu, Guo-Cheng & Gu, Xian-Ming, 2016. "Quadratic spline collocation method for the time fractional subdiffusion equation," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 252-265.
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    7. Yang, Xiao-Jun & Tenreiro Machado, J.A. & Srivastava, H.M., 2016. "A new numerical technique for solving the local fractional diffusion equation: Two-dimensional extended differential transform approach," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 143-151.
    8. Wang, Yanxin & Zhu, Li, 2016. "SCW method for solving the fractional integro-differential equations with a weakly singular kernel," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 72-80.
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