From the integral and differential calculus to the fractional differential equations

• Grant number: 16/07703-5
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Effective date (Start): July 01, 2016
• Effective date (End): June 30, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Rubens de Figueiredo Camargo
• Grantee: Giovana Pereira Vizotto
• Host Institution: Faculdade de Ciências (FC). Universidade Estadual Paulista (UNESP). Campus de Bauru. Bauru , SP, Brazil

Abstract

This study focuses on the basics of differential and integral calculus past the limit concepts, derivative and integral and its applications for later study differential equations and their applications in real problems, more specifically, the mathematical modeling and methodology of integral Laplace transform addressing its definition, properties, theorems of convolution and applications, as well as working with the problem of reversing this transformed. In addition, it intends to extend the project for another year, to begin the study of fractional calculus and differential equations of non-integer order. Finally, it is intended that the LaTeX and Mathematica programs are used in the development of this project, which will be valuable for this and future scientific work of candidate.