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Fractional conformable derivatives of Liouville–Caputo type with low-fractionality

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  • Morales-Delgado, V.F.
  • Gómez-Aguilar, J.F.
  • Escobar-Jiménez, R.F.
  • Taneco-Hernández, M.A.

Abstract

This paper presents a novel fractional conformable derivative of Liouville–Caputo type of fractional order α=n−ϵ that contains a small ϵ and positive integer n values between [1;2]. The method is applied to obtain analytical solutions for the electrical circuits LC and RL and for the equations that describe the motion of a charged particle in an electromagnetic field using an expansion of the fractional conformable derivative in ϵ=n−α. Numerical simulations were obtained for different values of the fractional order and the parameter ϵ. This novel fractional conformable derivative allows describing physical systems where the level of fractality is low, such as oscillators, quantum dynamics, electromagnetic fields, mechanics of fractal and complex media, among others.

Suggested Citation

  • Morales-Delgado, V.F. & Gómez-Aguilar, J.F. & Escobar-Jiménez, R.F. & Taneco-Hernández, M.A., 2018. "Fractional conformable derivatives of Liouville–Caputo type with low-fractionality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 424-438.
    • Handle: RePEc:eee:phsmap:v:503:y:2018:i:c:p:424-438
    DOI: 10.1016/j.physa.2018.03.018
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    References listed on IDEAS

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    Cited by:

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    2. Kumar, Sachin & Pandey, Prashant, 2020. "A Legendre spectral finite difference method for the solution of non-linear space-time fractional Burger’s–Huxley and reaction-diffusion equation with Atangana–Baleanu derivative," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    3. Owolabi, Kolade M. & Pindza, Edson, 2019. "Modeling and simulation of nonlinear dynamical system in the frame of nonlocal and non-singular derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 146-157.
    4. Kaya, Guven & Kartal, Senol & Gurcan, Fuat, 2020. "Dynamical analysis of a discrete conformable fractional order bacteria population model in a microcosm," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    5. Zeid, Samaneh Soradi, 2019. "Approximation methods for solving fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 171-193.
    6. Abdeljawad, Thabet & Al-Mdallal, Qasem M. & Jarad, Fahd, 2019. "Fractional logistic models in the frame of fractional operators generated by conformable derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 94-101.

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