Non-integer order derivatives applied to modeling

• Grant number: 21/03424-2
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Effective date (Start): September 01, 2021
• Effective date (End): April 30, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Rubens de Figueiredo Camargo
• Grantee: Matheus Pereira de Melo
• Host Institution: Faculdade de Ciências (FC). Universidade Estadual Paulista (UNESP). Campus de Bauru. Bauru , SP, Brazil

Abstract

The objective is to study integrals and derivatives of non-integer order, I. e, the so-called Fractional Calculus, its origin, main definitions, and properties, aiming to work the modeling made with non-integer differential equations, in order to refine the description given by the respective whole order equation and analyze the important dimensional issue arising from this modeling. With regard to applications, in addition to solving ordinary differential equations arising from engineering, biology, and economic problems, it is intended to propose and study, with due dimensional concern, the fractional version of these equations and to compare their solutions with the respective solutions of whole order in order to verify which fractional derivative order makes the description of the original problem more realistic. In addition, it is intended to analyze specific issues related to the dimension of fractional systems. Finally, it is highlighted that the programs LaTeX and Mathematica will be used in the development of this project, which will be of great value for this and future scientific works of the candidate, who has academic intentions. (AU)