From the usual calculus to the fractional modelling with dimensional analyze

• Grant number: 18/01729-8
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: April 01, 2018
• End date: December 31, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Rubens de Figueiredo Camargo
• Grantee: Jessica Caroline Fernandes
• Host Institution: Faculdade de Ciências (FC). Universidade Estadual Paulista (UNESP). Campus de Bauru. Bauru , SP, Brazil

Abstract

We aim to study integrals and derivatives of non-integer order, i. e, the so-called Fractional Calculus, its origin, main definitions and properties, aiming to study the modeling with differential equations of non-integer order, in order to refine the description given by the respective integer order and to analyze the dimensional of those models. 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 in 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 dimension of fractional systems. Finally, it is intended that the LaTeX and Mathematica programs to 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. (AU)