Dynamical and computational analysis of fractional order mathematical model for oscillatory chemical reaction in closed vessels

Abstract

One of the most fascinating chemical reactions is an oscillating one. The reactant and the autocatalyst are the two chemical species that are considered in this system. Firstly, we convert the oscillatory chemical reaction model into a fractional order oscillatory chemical reaction model for derivatives of arbitrary order provided in the sense of Caputo. The recommended methodology is centered on the shifted Jacobi collocation technique (JCT) and the shifted Jacobi operational matrix. In this work, we offer computational simulations of fractional order oscillatory chemical reaction models by using collocation technique and Newton polynomial interpolation (NPI) technique. The primary benefit of the collocation method is to study a general estimation for temporal and spatial discretizations. The numerical strategy also simplifies fractional differentiation equations (FDEs) by simplifying them into a simple issue that can be resolved by finding solutions to a few algebraic equations. We also present a comparison between the collocation and NPI techniques through the figures. The mathematical outcomes and data demonstrate that the offered strategy is an efficient procedure with outstanding reliability for resolving differential equations of arbitrary order. Some theorems related to the analysis of the collocation technique are also presented and explained here.