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Fractional differential equations in Engineering

Grant number: 14/24743-5
Support type:Scholarships in Brazil - Scientific Initiation
Effective date (Start): January 01, 2015
Effective date (End): December 31, 2015
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Applied Mathematics
Principal Investigator:Rubens de Figueiredo Camargo
Grantee:Rodrigo Ribeiro Bertolotto
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, the mathematical modeling and the methodology of the integral Laplace transform, addressing its definition, properties, theorems of convolution and applications as well as work with the problem of inversion this transformed. In addition, we intend to study integrals and derivatives of non-integer order, the so-called fractional calculus, its origin, main definitions and properties, aiming to work his modeling with non-integer order differential equations in order to refine the description given by its equation of entire order. With respect to applications, solving ordinary differential equations resulting from engineering problems, aims to propose and to study the fractional version of these equations and their solutions to compare their solutions integer order to verify that the order of derivative fractional which makes more realistic description of the original problem.