Fuzzy differential equations with interactive derivatives on time scales

• Grant number: 22/00196-1
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: September 01, 2022
• End date: August 31, 2025
• Field of knowledge: Physical Sciences and Mathematics - Computer Science - Computational Mathematics
• Principal Investigator: Estevão Esmi Laureano
• Grantee: Mina Shahidi
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Company: Universidade Estadual de Campinas (UNICAMP). Faculdade de Engenharia Elétrica e de Computação (FEEC)
• Associated research grant: 20/09838-0 - BI0S - Brazilian Institute of Data Science, AP.PCPE

Abstract

Fuzzy set theory is a mathematical field designed to analysing and processing sets (concepts) with uncertain boundaries. Recently, researchers have investigated solutions of dynamic systems in which their parameters and/or variables have values into the class of fuzzy numbers on time scales. In this project, we propose new definitions for derivative of fuzzy functions on time scales, where the values of their range may have a special type of relationship called interactivity. Are studiedtwo forms of interactivity: via the concept of completely correlated and linearly correlated fuzzy numbers. We introduce some properties of the proposed notions of differentiability. In addition, we show the connections between these derivatives and compare them with other well-known derivatives on time scales. We also present the characterization theorem of the new derivatives in terms of the Hilger differentiability of their endpoint functions. Furthermore, we establish theorems as the fundamental theorem of calculus. Finally, we study the fuzzy differential equations (FDEs) under the concepts of proposed differentiability on time scales that have coefficients and/or initial conditions uncertain and modeled by interactive fuzzy sets. In particular, we focus on HIV dynamics with imprecise factors such as mortality rate of the virus, presenting a fuzzy solution on time scales.

Scientific publications

(4)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

SHAHIDI, M.; ESMI, E.; BARROS, L. C.. A study on fuzzy Volterra integral equations for S-correlated fuzzy processes on time scales. FUZZY SETS AND SYSTEMS, v. 471, p. 24-pg., 2023-09-04. (22/00196-1, 20/09838-0)

SHAHIDI, M.; ESMI, E.. On the existence of approximate solutions to fuzzy delay differential equations under the metric derivative. COMPUTATIONAL & APPLIED MATHEMATICS, v. 41, n. 8, p. 16-pg., 2022-12-01. (22/00196-1, 20/09838-0)

SHAHIDI, M.; BARROS, L. C.; ESMI, E.. Linear fuzzy partial differential equations for..-linearly correlated fuzzy processes. INFORMATION SCIENCES, v. 691, p. 17-pg., 2024-11-13. (20/09838-0, 22/00196-1)

SHAHIDI, M.; ALLAHVIRANLOO, T.; ARANA-JIMENEZ, M.. Calculus and study of fuzzy dynamic equations for fuzzy vector functions on time scales. FUZZY SETS AND SYSTEMS, v. 507, p. 23-pg., 2025-05-01. (22/00196-1)