New developments on the theory of non-absolute integration of Henstock-Kurzweil and applications to differential and integral equations

• Grant number: 22/01214-3
• Support Opportunities: Scholarships abroad - Research
• Start date: April 01, 2022
• End date: May 15, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Márcia Cristina Anderson Braz Federson
• Grantee: Márcia Cristina Anderson Braz Federson
• Host Investigator: Tepper L. Gill
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Institution abroad: Howard University, United States

Abstract

Our research project is located in Mathematical Analysis, more specifically, in the area of Non-Absolute Integration related to the Henstock-Kurzweil integral and applications of this theory to differential and integral equations. The main objective of this project is to continue our scientific research in the development of the theory and applications of the Henstock-Kurzweil integral. In particular, we are interested in the further development of the theory of Generalized ODEs, based on the Kurzweil integral, and its applications to other types of differential and integral equations and to Physics. This project will be carried out in collaboration with Professor Tepper Gill at Howard University, in Washington DC, United States. The period foreseen for the development of scientific visits is from April 1, 2022 to May 15, 2022, totaling 1.5 months.Professor Gill has research experience with an extension of the Feynman integral via time-ordered operators and also works with Kuelbs-Steadman spaces. During our scientific visit, we intend to: * To describe and investigate the integral form of stochastic differential equations with integrands in Kuelbs-Steadman spaces, in collaboration with Professor Gill. (AU)