Numerical and computational analysis of fractional order mathematical models for chemical kinetics and carbon dioxide absorbed into phenyl glycidyl ether

Abstract

The major objective of this effort is to use the collocation technique (CT) to examine fractional chemical kinetics(CK) and other problem that correlates the condensations of carbon dioxide (CO2) and phenyl glycidyl ether (PGE) with two varieties of Dirichlet and a mixed set of Neumann boundary and Dirichlet-type constraints respectively. The suggested approach depends on the shifted Jacobi collocation techniques along with the shifted Jacobi operational matrix for fractional derivatives of any order, defined in the Caputo sense. Examining a global approximation for temporal and spatial discretizations is the main benefit of the suggested methodology. Additionally, the mathematical method simplifies the fractional differential equations by reducing them to a straightforward problem that just needs the solution of a set of algebraic equations. The arithmetical results and figures show that the suggested approach is an effective algorithm with excellent accuracy for resolving arbitrary order differential equations. A few theorems regarding error analysis are presented and explained. We also compare the numerical results produced using the suggested technique with those results obtained through the existing techniques.