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

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Kumar P., Govindaraj V., Ertürk V. S., Abdellattif M. H.

PRAMANA-JOURNAL OF PHYSICS, vol.96, no.3, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 96 Issue: 3
  • Publication Date: 2022
  • Doi Number: 10.1007/s12043-022-02359-2
  • Journal Name: PRAMANA-JOURNAL OF PHYSICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, Civil Engineering Abstracts
  • Keywords: Alkali-silica reaction, concrete, fractional-order mathematical model, Caputo fractional derivative, existence and uniqueness, Adams-Bashforth-Moulton scheme, 82, 40, Bj, 05, 45, -a, 82, 20, Wt, 02, 60, Lj, MODEL
  • Ondokuz Mayıs University Affiliated: Yes

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.