Affiliations: [a] Institute of Applied Social Sciences, Federal University of Alfenas, Varginha, Minas Gerais, Brazil
| [b] Department of Applied Mathematics, University of Campinas, Campinas, São Paulo, Brazil
| [c] Patagonia Campus, University Austral of Chile, Coyhaique, Aysén, Chile
Correspondence:
[*]
Corresponding author. Silvio Antônio Bueno Salgado, Institute of Applied Social Sciences, Federal University of Alfenas, Varginha, Minas Gerais 37130-001, Brazil. E-mail: [email protected].
Abstract: In this paper, we consider a type of fuzzy harmonic oscillator described by a differential equation of the form x″ + a2x = 0 with initial conditions given by fuzzy numbers. Here, we assume that x″ (t) and a2x (t) are linearly correlated fuzzy numbers for
t∈ℝ
and
a∈ℝ,a≠0
. In general, this assumption is necessary for the equality x″ + a2x = 0 to make sense. Using this interactive relation, we obtain a solution for this problem using a fuzzy Laplace transform method.
