On the Properties of the Semigroup Generated by the RL Fractional Integral

2024/04/24 by Kyan Ka Hin Cheung, Cheung, Kyan Ka Hin, Ethan Jon Yi Soh +1
Mathematics · #Functional Equations Stability Results #Nonlinear Differential Equations Analysis #Fractional Differential Equations Solutions

paper · pdf · doi:10.48550/arxiv.2405.05265

Abstract

For operators A, it is sometimes possible to define e^At as an operator in and of itself provided it meets certain regularity conditions. Like e^λx for ODEs, this operator is useful for solving PDEs involving the operator A. We call the set of e^At a semigroup generated by A. In this paper, we discuss the properties of semigroups generated by the fractional integral, an operator appearing in PDEs in increasingly many fields, over Bochner-Lebesgue spaces.

Related

• The Riemann-Liouville fractional integral in Bochner-Lebesgue spaces I
• Extension problem and fractional operators: semigroups and wave equations
• Sobolev spaces on arbitrary domains and semigroups generated by fractional Laplacian
• User's guide to the fractional Laplacian and the method of semigroups
• Semigroup property of fractional differential operators and its applications