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

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.