Introductory of fractional calculus and applications

• Grant number: 19/19722-2
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: December 01, 2019
• End date: March 31, 2021
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Marta Cilene Gadotti
• Grantee: Daniel de Lima Pazim
• Host Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil

Abstract

Motivated by the problem of the fractional harmonic oscillator, we intend to discuss certain approaches about fractional derivatives, and fractional integrals (simply called differintegral), ie the Riemann-Liouville, the Caputo and sequential approaches. The proposal is to build a theoretical framework in which the definition of the fractional derivative and, consequently, the differential equations with fractional derivatives and their properties will be discussed. We will consider some applications, which may include physical models.