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Numerical approximation of nonlinear fractional parabolic differential equations with Caputo–Fabrizio derivative in Riemann–Liouville sense

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  • Owolabi, Kolade M.
  • Atangana, Abdon

Abstract

This paper considers the Caputo–Fabrizio derivative in Riemann–Liouville sense for the spatial discretization fractional derivative. We formulate two notable exponential time differencing schemes based on the Adams–Bashforth and the Runge–Kutta methods to advance the fractional derivatives in time. Our approach is tested on a number of fractional parabolic differential equations that are of current and recurring interest, and which cover pitfalls and address points and queries that may naturally arise. The effectiveness and suitability of the proposed techniques are justified via numerical experiments in one and higher dimensions.

Suggested Citation

  • Owolabi, Kolade M. & Atangana, Abdon, 2017. "Numerical approximation of nonlinear fractional parabolic differential equations with Caputo–Fabrizio derivative in Riemann–Liouville sense," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 171-179.
    • Handle: RePEc:eee:chsofr:v:99:y:2017:i:c:p:171-179
    DOI: 10.1016/j.chaos.2017.04.008
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    References listed on IDEAS

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    1. Atangana, Abdon & Koca, Ilknur, 2016. "Chaos in a simple nonlinear system with Atangana–Baleanu derivatives with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 447-454.
    2. Kolade M. Owolabi & Kailash C. Patidar, 2015. "Existence and Permanence in a Diffusive KiSS Model with Robust Numerical Simulations," International Journal of Differential Equations, Hindawi, vol. 2015, pages 1-8, December.
    3. Alkahtani, B.S.T. & Atangana, A., 2016. "Controlling the wave movement on the surface of shallow water with the Caputo–Fabrizio derivative with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 539-546.
    4. Coronel-Escamilla, A. & Gómez-Aguilar, J.F. & López-López, M.G. & Alvarado-Martínez, V.M. & Guerrero-Ramírez, G.V., 2016. "Triple pendulum model involving fractional derivatives with different kernels," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 248-261.
    5. Gómez-Aguilar, J.F. & López-López, M.G. & Alvarado-Martínez, V.M. & Reyes-Reyes, J. & Adam-Medina, M., 2016. "Modeling diffusive transport with a fractional derivative without singular kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 467-481.
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    Cited by:

    1. Kholoud Saad Albalawi & Ibtehal Alazman & Jyoti Geetesh Prasad & Pranay Goswami, 2023. "Analytical Solution of the Local Fractional KdV Equation," Mathematics, MDPI, vol. 11(4), pages 1-13, February.
    2. Oscar Martínez-Fuentes & Fidel Meléndez-Vázquez & Guillermo Fernández-Anaya & José Francisco Gómez-Aguilar, 2021. "Analysis of Fractional-Order Nonlinear Dynamic Systems with General Analytic Kernels: Lyapunov Stability and Inequalities," Mathematics, MDPI, vol. 9(17), pages 1-29, August.

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