| Issue |
E3S Web Conf.
Volume 535, 2024
XIII International Scientific and Practical Forum “Environmental Aspects of Sustainability of Construction and Management of Urban Real Estate” (ESCM-2024)
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|
|---|---|---|
| Article Number | 01004 | |
| Number of page(s) | 9 | |
| Section | Innovative and Technical Solutions to Ensure Environmental Sustainability in Construction | |
| DOI | https://doi.org/10.1051/e3sconf/202453501004 | |
| Published online | 11 June 2024 | |
Neumann Problem for Second-Order Differential Equation with Fractional Derivative in the Analysis and Modeling of Structures Made of Viscoelastic Elements
Moscow State University of Civil Engineering, 26, Yaroslavskoye shosse, Moscow, 129337, Russia
1 Corresponding author: KiryanovaLV@mgsu.ru
This article addresses a second-order differential equation containing a Gerasimov-Kaputo fractional differentiation operator of order less than two. The Neumann problem is formulated for this equation. A system of eigenfunctions and eigenvalues for the considered homogeneous boundary problem of the second kind is found. A conjugate boundary problem for the Gerasimov-Kaputo fractional derivative is introduced. A biorthogonal system is obtained that is orthogonal to the found system of eigenfunctions. Visualizations of the eigenfunction system, biorthogonal system, and an example of eigenvalue distribution on the real axis are provided.
© The Authors, published by EDP Sciences, 2024
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