A new numerical technique for solving Caputo time-fractional biological population equation

Ali Khalouta; Abdelouahab Kadem; Ali Khalouta; Abdelouahab Kadem

doi:10.3934/math.2019.5.1307

AIMS Mathematics

2019, Volume 4, Issue 5: 1307-1319. doi: 10.3934/math.2019.5.1307

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A new numerical technique for solving Caputo time-fractional biological population equation

Ali Khalouta ^,,
Abdelouahab Kadem

Laboratory of Fundamental and Numerical Mathematics, Department of Mathematics, Faculty of Sciences, Ferhat Abbas University of Setif 1, Sétif 19000, Algeria

Received: 01 July 2019 Accepted: 16 August 2019 Published: 03 September 2019
MSC : Primary 35R11, 26A33; Secondary 74G10, 34K28

In this paper, we propose a new numerical technique called modified generalized Taylor fractional series method (MGTFSM) for solving Caputo time-fractional biological population equation.We present our obtained results in the form of a new theorem.This method based on constructing series solutions in a form of rapidly convergent series with easily computable components and without need of linearization, discretization, perturbation or unrealistic assumptions.The accuracy and efficiency of the method is tested by means of three numerical examples.The results prove that the proposed method is very effective and simple for solving fractional partial differential equations.
- biological population equation,
- Caputo fractional derivative,
- modified generalized Taylor fractional series method
Citation: Ali Khalouta, Abdelouahab Kadem. A new numerical technique for solving Caputo time-fractional biological population equation[J]. AIMS Mathematics, 2019, 4(5): 1307-1319. doi: 10.3934/math.2019.5.1307

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Abstract

In this paper, we propose a new numerical technique called modified generalized Taylor fractional series method (MGTFSM) for solving Caputo time-fractional biological population equation.We present our obtained results in the form of a new theorem.This method based on constructing series solutions in a form of rapidly convergent series with easily computable components and without need of linearization, discretization, perturbation or unrealistic assumptions.The accuracy and efficiency of the method is tested by means of three numerical examples.The results prove that the proposed method is very effective and simple for solving fractional partial differential equations.

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