Applied fractional modelling

• Grant number: 18/13969-3
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Effective date (Start): September 01, 2018
• Effective date (End): December 31, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Rubens de Figueiredo Camargo
• Grantee: Micaeli Mendola Theodoro
• 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. and the so-called Fractional Calculus, its origin, main definitions and properties, aiming to work the modeling done with differential equations of non-integer order, in order to refine the description given by the respective integer order and to analyze the important dimensional question arising 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 should be noted that the LaTeX and Mathematica programs will be used in the development of this project, which will be of great value to this and future scientific works of the candidate, who has academic pretensions.