Inverse problem for the time-fractional Euler-Bernoulli beam equation

• Published in: Mathematical modelling and analysis Vol. 26; no. 3; pp. 503 - 518
• Main Authors: Tekin, Ibrahim, Yang, He
• Format: Journal Article
• Language: English
• Published: Vilnius Vilnius Gediminas Technical University 01.09.2021
• Subjects: Boundary conditions; Calculus; Differential equations; Euler-Bernoulli beam; Euler-Bernoulli beams; existence and uniqueness; Existence theorems; Fractional calculus; inverse coefficient problem; Inverse problems; Mathematical analysis; Numerical analysis; Partial differential equations; Time dependence; Uniqueness theorems; Viscoelasticity; existence and uniqueness; inverse coefficient problem; Euler-Bernoulli beam
• ISSN: 1392-6292; 1648-3510
• DOI: 10.3846/mma.2021.13289

In this paper, the classical Euler-Bernoulli beam equation is considered by utilizing fractional calculus. Such an equation is called the time-fractional EulerBernoulli beam equation. The problem of determining the time-dependent coefficient for the fractional Euler-Bernoulli beam equation with homogeneous boundary conditions and an additional measurement is considered, and the existence and uniqueness theorem of the solution is proved by means of the contraction principle on a sufficiently small time interval. Numerical experiments are also provided to verify the theoretical findings.