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.