Next Article in Journal
A Discussion on p-Geraghty Contraction on mw-Quasi-Metric Spaces
Previous Article in Journal
High Capacity Reversible Data Hiding Based on the Compression of Pixel Differences
Previous Article in Special Issue
Coefficient Estimates for a Subclass of Analytic Functions Associated with a Certain Leaf-Like Domain
Open AccessArticle

A Comparative Study of the Fractional-Order Clock Chemical Model

1
Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
2
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40204, Taiwan
3
Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, Baku AZ1007, Azerbaijan
4
Department of Mathematics, College of Arts and Sciences, Najran University, Najran P.O. Box 1988, Saudi Arabia
5
Department of Mathematics, Faculty of Applied Science, Taiz University, Taiz P.O. Box 6803, Yemen
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(9), 1436; https://doi.org/10.3390/math8091436
Received: 3 August 2020 / Revised: 20 August 2020 / Accepted: 24 August 2020 / Published: 27 August 2020
In this paper, a comparative study has been made between different algorithms to find the numerical solutions of the fractional-order clock chemical model (FOCCM). The spectral collocation method (SCM) with the shifted Legendre polynomials, the two-stage fractional Runge–Kutta method (TSFRK) and the four-stage fractional Runge–Kutta method (FSFRK) are used to approximate the numerical solutions of FOCCM. Our results are compared with the results obtained for the numerical solutions that are based upon the fundamental theorem of fractional calculus as well as the Lagrange polynomial interpolation (LPI). Firstly, the accuracy of the results is checked by computing the absolute error between the numerical solutions by using SCM, TSFRK, FSFRK, and LPI and the exact solution in the case of the fractional-order logistic equation (FOLE). The numerical results demonstrate the accuracy of the proposed method. It is observed that the FSFRK is better than those by SCM, TSFRK and LPI in the case of an integer order. However, the non-integer orders in the cases of the SCM and LPI are better than those obtained by using the TSFRK and FSFRK. Secondly, the absolute error between the numerical solutions of FOCCM based upon SCM, TSFFRK, FSFRK, and LPI for integer order and non-integer order has been computed. The absolute error in the case of the integer order by using the three methods of the third order is considered. For the non-integer order, the order of the absolute error in the case of SCM is found to be the best. Finally, these results are graphically illustrated by means of different figures. View Full-Text
Keywords: fractional derivatives; fractional-order clock chemical model; shifted Legendre polynomials; spectral collocation method; Lagrange polynomial interpolation; fractional Runge-Kutta method; Newton-Raphson method fractional derivatives; fractional-order clock chemical model; shifted Legendre polynomials; spectral collocation method; Lagrange polynomial interpolation; fractional Runge-Kutta method; Newton-Raphson method
Show Figures

Figure 1

MDPI and ACS Style

Srivastava, H.M.; Saad, K.M. A Comparative Study of the Fractional-Order Clock Chemical Model. Mathematics 2020, 8, 1436. https://doi.org/10.3390/math8091436

AMA Style

Srivastava HM, Saad KM. A Comparative Study of the Fractional-Order Clock Chemical Model. Mathematics. 2020; 8(9):1436. https://doi.org/10.3390/math8091436

Chicago/Turabian Style

Srivastava, Hari M.; Saad, Khaled M. 2020. "A Comparative Study of the Fractional-Order Clock Chemical Model" Mathematics 8, no. 9: 1436. https://doi.org/10.3390/math8091436

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop