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Fractional Calculus and Bernoullis Differential Equation.

Grant number: 12/07316-0
Support type:Scholarships in Brazil - Scientific Initiation
Effective date (Start): May 01, 2012
Effective date (End): April 30, 2013
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Applied Mathematics
Principal Investigator:Rubens de Figueiredo Camargo
Grantee:Bruno Rodrigo Martins
Home Institution: Faculdade de Ciências (FC). Universidade Estadual Paulista (UNESP). Campus de Bauru. Bauru , SP, Brazil

Abstract

This study focuses on differential equations and their applications in problems related to engineering, more specifically, to study the mathematical modeling and methodology of integral transforms of Laplace and Fourier, addressing their definitions, conditions of existence, properties, and applications of convolution theorems. In addition, we intend to study full order derivatives and non-integer, the so-called fractional calculus, its origin, the main definitions and properties, aiming to work his modeling differential equations with non-integer order, in order to refine the description given by its equation of entire order. With regard to applications, solving ordinary differential equations arising in engineering problems, we intend to propose and solve the fractional version of the classic Bernoulli ordinary differential equation and recover the classical solution as a particular case.