Open AccessINVERSE PROBLEM FOR THE TIME-FRACTIONAL EULER-BERNOULLI BEAM EQUATION
Author(s) -
İbrahim Tekin,
Yihua He
Publication year - 2021
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/mma.2021.13289
Subject(s) - mathematics , bernoulli's principle , mathematical analysis , uniqueness , euler's formula , uniqueness theorem for poisson's equation , contraction (grammar) , boundary value problem , inverse problem , beam (structure) , fractional calculus , physics , medicine , optics , thermodynamics
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.