A Fractional-Order Chemical System: Numerical Analysis with Distinct Variable-Order Derivatives

Ughur Budaq; Emrullah Yaşar

doi:10.33187/jmsm.1749478

A Fractional-Order Chemical System: Numerical Analysis with Distinct Variable-Order Derivatives

Abstract

Fractional calculus models complicated systems that exhibit memory effects, showing much greater potential than classical integer-order derivatives in modeling chaotic systems. In this study, we investigate the application of two numerical interpolation methods, Newton and Lagrange polynomials, for solving a fractional-order Lorenz-type chemical model based on various fractional derivatives. The Lorenz-type model is modified, as it is known for its chaotic behavior, and augmented to allow for modeling chemical reactions, with variable-order fractional derivatives to reflect reality. We utilize numerical schemes for the Caputo-Liouville, Caputo-Fabrizio, and Atangana-Baleanu-Caputo fractional derivatives, and we assess the performance of the Newton and the Lagrange numerical approximations.

Keywords

Chemical system, Fractional calculus, Fractional derivative, Lagrange interpolation, Newton interpolation

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Details

Primary Language

English

Subjects

Applied Mathematics (Other)

Journal Section

Research Article

Authors

Ughur Budaq
0009-0007-5482-1436
Türkiye

Emrullah Yaşar ^*
0000-0003-4732-5753
Türkiye

Early Pub Date

October 21, 2025

Publication Date

December 15, 2025

Submission Date

July 23, 2025

Acceptance Date

September 29, 2025

Published in Issue

Year 2025 Volume: 8 Number: 4

DOI

https://doi.org/10.33187/jmsm.1749478

IZ

https://izlik.org/JA78HU29TD

APA

Budaq, U., & Yaşar, E. (2025). A Fractional-Order Chemical System: Numerical Analysis with Distinct Variable-Order Derivatives. Journal of Mathematical Sciences and Modelling, 8(4), 185-194. https://doi.org/10.33187/jmsm.1749478

AMA

1.Budaq U, Yaşar E. A Fractional-Order Chemical System: Numerical Analysis with Distinct Variable-Order Derivatives. Journal of Mathematical Sciences and Modelling. 2025;8(4):185-194. doi:10.33187/jmsm.1749478

Chicago

Budaq, Ughur, and Emrullah Yaşar. 2025. “A Fractional-Order Chemical System: Numerical Analysis With Distinct Variable-Order Derivatives”. Journal of Mathematical Sciences and Modelling 8 (4): 185-94. https://doi.org/10.33187/jmsm.1749478.

EndNote

Budaq U, Yaşar E (December 1, 2025) A Fractional-Order Chemical System: Numerical Analysis with Distinct Variable-Order Derivatives. Journal of Mathematical Sciences and Modelling 8 4 185–194.

IEEE

[1]U. Budaq and E. Yaşar, “A Fractional-Order Chemical System: Numerical Analysis with Distinct Variable-Order Derivatives”, Journal of Mathematical Sciences and Modelling, vol. 8, no. 4, pp. 185–194, Dec. 2025, doi: 10.33187/jmsm.1749478.

ISNAD

Budaq, Ughur - Yaşar, Emrullah. “A Fractional-Order Chemical System: Numerical Analysis With Distinct Variable-Order Derivatives”. Journal of Mathematical Sciences and Modelling 8/4 (December 1, 2025): 185-194. https://doi.org/10.33187/jmsm.1749478.

JAMA

1.Budaq U, Yaşar E. A Fractional-Order Chemical System: Numerical Analysis with Distinct Variable-Order Derivatives. Journal of Mathematical Sciences and Modelling. 2025;8:185–194.

MLA

Budaq, Ughur, and Emrullah Yaşar. “A Fractional-Order Chemical System: Numerical Analysis With Distinct Variable-Order Derivatives”. Journal of Mathematical Sciences and Modelling, vol. 8, no. 4, Dec. 2025, pp. 185-94, doi:10.33187/jmsm.1749478.

Vancouver

1.Ughur Budaq, Emrullah Yaşar. A Fractional-Order Chemical System: Numerical Analysis with Distinct Variable-Order Derivatives. Journal of Mathematical Sciences and Modelling. 2025 Dec. 1;8(4):185-94. doi:10.33187/jmsm.1749478