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

Abdon Atangana and Rubayyi T. Alqahtani

Chaos, Solitons & Fractals, 2018, vol. 116, issue C, 14-21

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.

Keywords: Fractional calculus; Fundamental theorem of fractional calculus; Lagrange polynomial; Keller-Segel model (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (10)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:116:y:2018:i:c:p:14-21

DOI: 10.1016/j.chaos.2018.09.013

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