Fractional calculus: applications dimensional analysis

• Grant number: 18/02069-1
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Effective date (Start): March 01, 2018
• Effective date (End): February 28, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Rubens de Figueiredo Camargo
• Grantee: Thais Hermoso de Oliveira
• 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, ie, the so-called fractional Calculus, its origin, main definitions and properties, aiming to work the modeling done with non-integer differential equations, in order to refine the description given by the respective equation and to analyze the important dimensional question that comes from this modeling. In terms of applications, in addition to solving ordinary differential equations arising from engineering, biology and economics problems, we intend to propose and study, with due dimensional concern, the fractional version of these equations and compare their solutions with the respective solutions. Order to check the order of the fractional derivative that makes the description of the original problem more realistic. In addition, we intend to analyze, specific questions regarding the size of fractional systems. Finally, it is intended that the LaTeX and Mathematica programs 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 pretensions. Eventually, this project will be renewable for another year and it is emphasized that, in the course of the work, other problems and applications may arise in a way to complement the study carried out, especially with problems related to meteorology, which is the course of the candidate . (AU)