Fractional Calculus for Non-Discrete Signed Measures

Author:

Kolokoltsov Vassili N.12ORCID,Shishkina Elina L.34ORCID

Affiliation:

1. Faculty of Computation Mathematics and Cybernetics, Lomonosov Moscow State University, 119991 Moscow, Russia

2. Moscow Center of Fundamental and Applied Mathematics, 119234 Moscow, Russia

3. Department of Mathematical and Applied Analysis, Voronezh State University, 394018 Voronezh, Russia

4. Department of Applied Mathematics and Computer Modeling, Belgorod State National Research University (BelGU), 308015 Belgorod, Russia

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. This article provides examples of semigroups based on integral operators with signed measures and discusses the fractional powers of differential operators with partial derivatives.

Publisher

MDPI AG

Reference28 articles.

1. Samko, S.G., Kilbas, A.A., and Marichev, O.I. (1993). Fractional Integrals and Derivatives, Gordon and Breach Science Publishers.

2. The Probabilistic Point of View on the Generalized Fractional Partial Differential Equations;Kolokoltsov;Fract. Calc. Appl. Anal.,2019

3. Klages, R., Radons, G., and Sokolov, I.M. (2008). Anomalous Transport: Foundations and Applications, Wiley-VCH Verlag GmbH & Co. KGaA.

4. An operational calculus for infinitesimal generators of semigroups;Balakrishnan;Trans. Amer. Math. Soc.,1959

5. Krasnoselski, M.A., Zabreyko, P.P., Pustilnik, E.I., and Sobolevski, P.S. (1966). Integral Operators in the Spaces of Summable Functions, Nauka.

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3