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On the analytical solutions of the system of conformable time-fractional Robertson equations with 1-D diffusion

Author

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  • Iyiola, O.S.
  • Tasbozan, O.
  • Kurt, A.
  • Çenesiz, Y.

Abstract

In this paper, we consider the system of conformable time-fractional Robertson equations with one-dimensional diffusion having widely varying diffusion coefficients. Due to the mismatched nature of the initial and boundary conditions associated with Robertson equation, there are spurious oscillations appearing in many computational algorithms. Our goal is to obtain an approximate solutions of this system of equations using the q-homotopy analysis method (q-HAM) and examine the widely varying diffusion coefficients and the fractional order of the derivative.

Suggested Citation

  • Iyiola, O.S. & Tasbozan, O. & Kurt, A. & Çenesiz, Y., 2017. "On the analytical solutions of the system of conformable time-fractional Robertson equations with 1-D diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 94(C), pages 1-7.
    • Handle: RePEc:eee:chsofr:v:94:y:2017:i:c:p:1-7
    DOI: 10.1016/j.chaos.2016.11.003
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    References listed on IDEAS

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    1. Lenzi, E.K. & Menechini Neto, R. & Tateishi, A.A. & Lenzi, M.K. & Ribeiro, H.V., 2016. "Fractional diffusion equations coupled by reaction terms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 458(C), pages 9-16.
    2. Lokenath Debnath, 2003. "Recent applications of fractional calculus to science and engineering," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-30, January.
    3. 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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    Cited by:

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    2. Ahmed A. El-Deeb & Jan Awrejcewicz, 2021. "Steffensen-Type Inequalities with Weighted Function via ( γ , a )-Nabla-Conformable Integral on Time Scales," Mathematics, MDPI, vol. 9(23), pages 1-15, November.
    3. Thabet, Hayman & Kendre, Subhash, 2018. "Analytical solutions for conformable space-time fractional partial differential equations via fractional differential transform," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 238-245.
    4. Zhao, Dazhi & Yu, Guozhu & Tian, Yan, 2020. "Recursive formulae for the analytic solution of the nonlinear spatial conformable fractional evolution equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    5. Baogui Xin & Wei Peng & Yekyung Kwon & Yanqin Liu, 2019. "Modeling, discretization, and hyperchaos detection of conformable derivative approach to a financial system with market confidence and ethics risk," Papers 1903.12267, arXiv.org, revised Apr 2019.
    6. Korkmaz, Alper, 2017. "Exact solutions of space-time fractional EW and modified EW equations," Chaos, Solitons & Fractals, Elsevier, vol. 96(C), pages 132-138.
    7. Khaled, Khachnaoui, 2021. "Nehari type solutions for fractional Hamiltonian systems," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).

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