Solution of a fuzzy differential equation with interactivity via Laplace transform

Author(s)

Bueno Salgado, Silvio Antonio ^[1] ; de Barros, Laecio Carvalho ^[2] ; Esmi, Estevao ^[2] ; Eduardo Sanchez, Daniel ^[3]

Affiliation

^[1] Univ Fed Alfenas, Inst Appl Social Sci, BR-37130001 Varginha, MG - Brazil

^[2] Univ Estadual Campinas, Dept Appl Math, Campinas, SP - Brazil

^[3] Univ Austral Chile, Patagonia Campus, Aysen - Chile

• Document type: Journal article
• Source: JOURNAL OF INTELLIGENT & FUZZY SYSTEMS; v. 37, n. 2, p. 2495-2501, 2019.
• Web of Science Citations: 0

Abstract

In this paper, we consider a type of fuzzy harmonic oscillator described by a differential equation of the form x `' a(2)x = 0 with initial conditions given by fuzzy numbers. Here, we assume that x `'(t) and a(2)x(t) are linearly correlated fuzzy numbers for t is an element of R and a is an element of R, a not equal 0. In general, this assumption is necessary for the equality x `' a(2)x = 0 to make sense. Using this interactive relation, we obtain a solution for this problem using a fuzzy Laplace transform method. (AU)

• FAPESP's process: 16/26040-7 - Differential and integral calculus based on arithmetic of interactive fuzzy numbers
• Grantee: Estevão Esmi Laureano
• Support Opportunities: Regular Research Grants
• FAPESP's process: 18/10946-2 - The 13th International FLINS Conference on Data Science and Knowledge Engineering for Sensing Decision Support
• Grantee: Laécio Carvalho de Barros
• Support Opportunities: Research Grants - Meeting - Abroad