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Collocation methods for fractional differential equations involving non-singular kernel

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  • Baleanu, D.
  • Shiri, B.

Abstract

A system of fractional differential equations involving non-singular Mittag-Leffler kernel is considered. This system is transformed to a type of weakly singular integral equations in which the weak singular kernel is involved with both the unknown and known functions. The regularity and existence of its solution is studied. The collocation methods on discontinuous piecewise polynomial space are considered. The convergence and superconvergence properties of the introduced methods are derived on graded meshes. Numerical results provided to show that our theoretical convergence bounds are often sharp and the introduced methods are efficient. Some comparisons and applications are discussed.

Suggested Citation

  • Baleanu, D. & Shiri, B., 2018. "Collocation methods for fractional differential equations involving non-singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 136-145.
    • Handle: RePEc:eee:chsofr:v:116:y:2018:i:c:p:136-145
    DOI: 10.1016/j.chaos.2018.09.020
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    References listed on IDEAS

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    1. Sandev, Trifce & Tomovski, Živorad & Dubbeldam, Johan L.A., 2011. "Generalized Langevin equation with a three parameter Mittag-Leffler noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(21), pages 3627-3636.
    2. Kundu, Snehasis, 2018. "Suspension concentration distribution in turbulent flows: An analytical study using fractional advection–diffusion equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 135-155.
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    Cited by:

    1. Alijani, Zahra & Baleanu, Dumitru & Shiri, Babak & Wu, Guo-Cheng, 2020. "Spline collocation methods for systems of fuzzy fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    2. Ariza-Hernandez, Francisco J. & Martin-Alvarez, Luis M. & Arciga-Alejandre, Martin P. & Sanchez-Ortiz, Jorge, 2021. "Bayesian inversion for a fractional Lotka-Volterra model: An application of Canadian lynx vs. snowshoe hares," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    3. Shiri, B. & Baleanu, D., 2019. "System of fractional differential algebraic equations with applications," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 203-212.
    4. Abdelkawy, M.A. & Lopes, António M. & Babatin, Mohammed M., 2020. "Shifted fractional Jacobi collocation method for solving fractional functional differential equations of variable order," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    5. Zeid, Samaneh Soradi, 2019. "Approximation methods for solving fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 171-193.

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