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New numerical method and application to Keller-Segel model with fractional order derivative

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  • Atangana, Abdon
  • Alqahtani, Rubayyi T.

Abstract

Using the fundamental theorem of fractional calculus together with the well-known Lagrange polynomial interpolation, we constructed a new numerical scheme. The new numerical scheme is suggested to solve non-linear and linear partial differential equation with fractional order derivative. The method was used to solve numerically the time fractional Keller-Segel model. The existence and uniqueness solution of the model with fractional Mittag-Leffler kernel derivative are presented in detail. Some simulations are performed to access the efficiency of the newly proposed method.

Suggested Citation

  • Atangana, Abdon & Alqahtani, Rubayyi T., 2018. "New numerical method and application to Keller-Segel model with fractional order derivative," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 14-21.
    • Handle: RePEc:eee:chsofr:v:116:y:2018:i:c:p:14-21
    DOI: 10.1016/j.chaos.2018.09.013
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    References listed on IDEAS

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    1. Abdeljawad, Thabet & Baleanu, Dumitru, 2017. "Monotonicity analysis of a nabla discrete fractional operator with discrete Mittag-Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 106-110.
    2. 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.
    3. Al-Mdallal, Qasem M. & Abu Omer, Ahmed S., 2018. "Fractional-order Legendre-collocation method for solving fractional initial value problems," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 74-84.
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    Cited by:

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