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Modeling of Strength Characteristics of Polymer Concrete Via the Wave Equation with a Fractional Derivative

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  • Ludmila Kirianova

    (Department of Applied Mathematics, Moscow State University of Civil Engineering, 129337 Moscow, Russia)

Abstract

The article presents a solution to a boundary value problem for a wave equation containing a fractional derivative with respect to a spatial variable. This model is used to describe oscillation processes in a viscoelastic medium, in particular changes in the deformation-strength characteristics of polymer concrete (dian and dichloroanhydride-1,1-dichloro-2,2-diethylene) under the influence of the gravity force. Based on the obtained solution to the boundary value problem, the article presents four numerical examples corresponding to homogeneous boundary conditions and various initial conditions. The graphs of the found solutions were constructed and the calculation accuracy in the considered examples was estimated.

Suggested Citation

  • Ludmila Kirianova, 2020. "Modeling of Strength Characteristics of Polymer Concrete Via the Wave Equation with a Fractional Derivative," Mathematics, MDPI, vol. 8(10), pages 1-10, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1843-:d:431572
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    References listed on IDEAS

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    1. Lina Song & Weiguo Wang, 2013. "Solution of the Fractional Black-Scholes Option Pricing Model by Finite Difference Method," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, June.
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    Cited by:

    1. Victor N. Orlov & Asmaa M. Elsayed & Elsayed I. Mahmoud, 2022. "Two Linearized Schemes for One-Dimensional Time and Space Fractional Differential Equations," Mathematics, MDPI, vol. 10(19), pages 1-16, October.

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