A study on the dynamics of alkali–silica chemical reaction by using Caputo fractional derivative

Abstract

In this paper, we propose a mathematical study to simulate the dynamics of alkali–silica reaction (ASR) by using the Caputo fractional derivative. We solve a non-linear fractional-order system containing six differential equations to understand the ASR. For proving the existence of a unique solution, we use some recent novel properties of Mittag–Leffler function along with the fixed point theory. The stability of the proposed system is also proved by using Ulam–Hyers technique. For deriving the fractional-order numerical solution, we use the well-known Adams–Bashforth–Moulton scheme along with its stability. Graphs are plotted to understand the given chemical reaction practically. The main reason to use the Caputo-type fractional model for solving the ASR system is to propose a novel mathematical formulation through which the ASR mechanism can be efficiently explored. This paper clearly shows the importance of fractional derivatives in the study of chemical reactions.