Open AccessMathematical model of the polymer concrete by fractional calculus with respect to a spatial variable
Author(s) -
Temirkhan Aleroev,
Elsayed I. Mahmoud,
Asmaa M. Elsayed
Publication year - 2021
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/1129/1/012031
Subject(s) - variable (mathematics) , fractional calculus , calculus (dental) , mathematics , computer science , mathematical analysis , medicine , dentistry
The article presents a solution of the vibration string equation containing the fractional derivative concerning the spatial variable, in which the fractional derivative is defined by Caputo. This model is utilized for characterizing the oscillation mechanical process in a viscoelastic medium. The theoretical solution is presented, and the fractional derivative parameter is determined. We compared the theoretical solution and the experimental data for polymer concrete samples. A sample of the problem of structural mechanics has been considered. This sample allows the demonstration of some advantages of the application of the suggested approach to solve the fractional vibration equation.