Work

Fractional Calculus for Non-Discrete Signed Measures

Year: 2024

Type: article

Abstract: In this paper we suggest a first ever construction of fractional integral and differential operators based on signed measures including a vector-valued case. The study focuses on constructing the fractional power of the Riemann-Stieltjes integral with a signed measure, using semigroup theory. The main result is a theorem that provides the exact form of a semigroup for the Riemann-Stieltjes integral with a measure having a countable number of extrema. The article provides examples of semigroups based on integral operators with signed measures and discusses the fractional powers of differential operators with partial derivatives.

Source: Mathematics

DOI: 10.3390/math12182804

Authors: Vassili N. Kolokoltsov, Elina Shishkina

Institutions: Lomonosov Moscow State University, Moscow Center of Fundamental and Applied Mathematics, Belgorod National Research University, Voronezh State University

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,955

Funders: Engineering and Physical Sciences Research Council, Division of Mathematical Sciences