Numerical Solutions of Fractional Order Autocatalytic Chemical Reaction Model

Mevlüde Yakıt Ongun; Damla Arslan; Javad Farzi

doi:10.19113/sdufbed.24679

Numerical Solutions of Fractional Order Autocatalytic Chemical Reaction Model

Abstract

The main concerns of this paper is the study and the development of numerical methods for solving fractional order autocatalytic chemical reaction model problem. This is a nonlinear fractional order differential equation of fractional order , where . Three different (explicit and implicit) schemes based on multistep methods, nonstandard finite difference method and the product integration (PI) method are developed. The PI scheme enjoys the integral equation formulation of the model problem. The accuracy, efficiency and comparison of the developed methods are demonstrated in numerical results.

Keywords

Fractional differential equations,Explicit and implicit methods; Product integrations methods; Nonstandard schemes; Brusselator model

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Details

Primary Language

Turkish

Subjects

-

Journal Section

-

Authors

Mevlüde Yakıt Ongun

Damla Arslan This is me

Javad Farzi This is me

Publication Date

April 15, 2017

Submission Date

June 29, 2016

Acceptance Date

-

Published in Issue

Year 2017 Volume: 21 Number: 1

DOI

https://doi.org/10.19113/sdufbed.24679

IZ

https://izlik.org/JA76ZK24JY

Cite

RIS / Bibtex

APA

Yakıt Ongun, M., Arslan, D., & Farzi, J. (2017). Numerical Solutions of Fractional Order Autocatalytic Chemical Reaction Model. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 21(1), 165-172. https://doi.org/10.19113/sdufbed.24679

AMA

1.Yakıt Ongun M, Arslan D, Farzi J. Numerical Solutions of Fractional Order Autocatalytic Chemical Reaction Model. J. Nat. Appl. Sci. 2017;21(1):165-172. doi:10.19113/sdufbed.24679

Chicago

Yakıt Ongun, Mevlüde, Damla Arslan, and Javad Farzi. 2017. “Numerical Solutions of Fractional Order Autocatalytic Chemical Reaction Model”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 21 (1): 165-72. https://doi.org/10.19113/sdufbed.24679.

EndNote

Yakıt Ongun M, Arslan D, Farzi J (April 1, 2017) Numerical Solutions of Fractional Order Autocatalytic Chemical Reaction Model. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 21 1 165–172.

IEEE

[1]M. Yakıt Ongun, D. Arslan, and J. Farzi, “Numerical Solutions of Fractional Order Autocatalytic Chemical Reaction Model”, J. Nat. Appl. Sci., vol. 21, no. 1, pp. 165–172, Apr. 2017, doi: 10.19113/sdufbed.24679.

ISNAD

Yakıt Ongun, Mevlüde - Arslan, Damla - Farzi, Javad. “Numerical Solutions of Fractional Order Autocatalytic Chemical Reaction Model”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 21/1 (April 1, 2017): 165-172. https://doi.org/10.19113/sdufbed.24679.

JAMA

1.Yakıt Ongun M, Arslan D, Farzi J. Numerical Solutions of Fractional Order Autocatalytic Chemical Reaction Model. J. Nat. Appl. Sci. 2017;21:165–172.

MLA

Yakıt Ongun, Mevlüde, et al. “Numerical Solutions of Fractional Order Autocatalytic Chemical Reaction Model”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, vol. 21, no. 1, Apr. 2017, pp. 165-72, doi:10.19113/sdufbed.24679.

Vancouver

1.Mevlüde Yakıt Ongun, Damla Arslan, Javad Farzi. Numerical Solutions of Fractional Order Autocatalytic Chemical Reaction Model. J. Nat. Appl. Sci. 2017 Apr. 1;21(1):165-72. doi:10.19113/sdufbed.24679

Cited By

Fractional Clique Collocation Technique for Numerical Simulations of Fractional-Order Brusselator Chemical Model

Axioms

https://doi.org/10.3390/axioms11110654