Analysing and solving the fractional Maxwell equations

• Grant number: 19/13691-8
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: September 01, 2019
• End date: August 31, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Alexys Bruno Alfonso
• Grantee: Marcelo Eduardo Benencase
• Host Institution: Faculdade de Ciências (FC). Universidade Estadual Paulista (UNESP). Campus de Bauru. Bauru , SP, Brazil

Abstract

This proposal deals with a computational and theoretical work. It is framed in Fractional Calculus, an emergent topic of Applied Mathematics, focusing applications in Physics and Electrical Engineering. The goal of this research project is to deepen the study of fractional-order Maxwell's equations, verify their consistency and investigate both stationary electromagnetic phenomena and wave propagation. The activities will start with studies on standard vector analysis and Maxwell's equations study, and will continue with an investigation of the fractional versions of Green's, Stokes's and Gauss's theorems. At its most important phase, the research will deal with the fracional order Maxwell's equations, to solve Poisson's equation and wave equation in rectangular and circular domains.The undergraduate applicant studies electrical engineering at UNESP, Bauru, has excelent mathematical and computational knowledge as well as great vocation to perform scientific research. By developing this project, the applicant will acquire scientific work skills and further knowledge about Calculus, Differential Equations, Integral Transforms, Numerical Analysis, Computational Programming and Electromagnetism.