Fractional calculus and the Mittag-Leffler functions

• Grant number: 18/13948-6
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Effective date (Start): November 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: Vitor Henrique Lopes Gusson
• Host Institution: Faculdade de Ciências (FC). Universidade Estadual Paulista (UNESP). Campus de Bauru. Bauru , SP, Brazil

Abstract

The objective of this project 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.