Ordinary and Fractional Differential Equations with Applications

• Grant number: 24/13630-7
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: October 01, 2024
• End date: January 31, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Marta Cilene Gadotti
• Grantee: Luca Alexandre Daroz
• Host Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil

Abstract

In this project, we initially intend to discuss classic and important results of the Qualitative Theory of ODE - Ordinary Differential Equations and then study similar results for the case of ODE - Fractional Differential Equations, especially those involving the Riemann-Liouville and Caputo derivatives. Finally, we will study mathematical models described by this type of equations, such as the harmonic oscillator model and biological models. Therefore, the proposal is to build a theoretical framework, in which results of existence and uniqueness of solution, continuous dependence with respect to the initial data and stability for this ODE and EDF and applications will be discussed.