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    • Keywords


      Alkali–silica reaction; concrete; fractional-order mathematical model; Caputo fractional derivative; existence and uniqueness; Adams–Bashforth–Moulton scheme.

    • 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 anovel 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.

    • Author Affiliations



      1. Department of Mathematics, National Institute of Technology Puducherry, Karaikal 609 609, India
      2. Department of Mathematics, Faculty of Arts and Sciences, Ondokuz Mayis University, Atakum 55200, Samsun, Turkey
      3. Department of Chemistry, College of Science, Taif University, Al-Haweiah, P.O. Box 11099, Taif 21944, Saudi Arabia
    • Dates

  • Pramana – Journal of Physics | News

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      Posted on July 25, 2019

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