Computational framework for analyzing fractional biochemical reaction model

Volume 36, Issue 2, pp 218--228 https://dx.doi.org/10.22436/jmcs.036.02.06

Publication Date: July 15, 2024 Submission Date: September 28, 2023 Revision Date: December 10, 2023 Accteptance Date: May 04, 2024

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Authors

D. Kumar S - Department of Mathematics, University of Rajasthan‎, Jaipur-302004, India. - Department of Mathematics‎, Kyung Hee University, 26 Kyungheedae-ro‎, ‎Dongdaemun-gu, Seoul‎, ‎02447, Korea. H. Nama - Department of Mathematics, University of Rajasthan‎, Near East Boulevard, PC: 99138, Jaipur-302004, India. D. Baleanu - Department of Computer Science and Mathematics‎, ‎Lebanese American University‎, Beirut‎, Lebanon. - Institute of Space Sciences-Subsidiary of INFLPR, ‎Magurele-Bucharest‎, Romania.

Abstract

‎The approximate numerical approach for the system of coupled nonlinear ordinary differential equations (ODEs) of a biochemical reaction model is very important for biochemists and scientist working in the field of biochemistry and related issues‎. ‎Within this article‎, ‎two computational algorithms for numerically solving a biochemical reaction model with time-fractional derivatives are examined and compared‎. ‎The first technique depends on the collocation method along with the shifted Jacobi operational matrix for fractional derivative defined in the Caputo sense‎, ‎and using this technique‎, ‎we created a system of algebraic equations from the given fractional model‎. ‎Another approach is centered on the basic theorem of fractional calculus and the characteristics of Newton's polynomial interpolation (NPI)‎. ‎We use these two methods to compute solution for the fractional biochemical reaction model‎. ‎The model's computational outcomes are compared by using the recommended techniques in this work‎. ‎Graphical and tabular forms are used to confirm the reliability and effectiveness of both techniques and an excellent match is discovered‎.

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Keywords

• Biochemical reaction model
• collocation technique
• Newton polynomial interpolation
• Jacobi operational matrix‎

MSC

•  26A33
•  33C45
•  65L05

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