Applications for the analytical inversion of the Laplace transform without contour integration

• Grant number: 16/05082-3
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: July 01, 2016
• End date: June 30, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Eliana Contharteze Grigoletto
• Grantee: Pedro Henrique de Oliveira Garcia
• Host Institution: Faculdade de Ciências Agronômicas (FCA). Universidade Estadual Paulista (UNESP). Campus de Botucatu. Botucatu , SP, Brazil

Abstract

From the calculation of inversion of the Laplace transform without contour integration in the complex plane, the objective is to express the Mittag-Leffler function, suitable for problems arising from the fractional calculus as a improper integral. As a result, a variety of convergent improper integrals of functions in terms of trigonometric functions can be expressed through the Mittag-Leffler functions. Still using this method of inversion of the Laplace transform without contour integration, intended to obtain the inverse Laplace transform for the non tabulated functions and in addition to developing an alternative method for the find the analytically solution of the ordinary or partial differential equation with the boundary conditions and/or initial conditions when we use the Laplace transform in resolution for the differential equation. This methodology is used, for example, to obtain information of the structure and molecular dynamics of physical, chemical and biological systems that occurs in a luminescence decay law.