THE RIEMANN-LIOUVILLE FRACTIONAL INTEGRAL IN BOCHNER-LEBESGUE SPACES I

被引：3

作者：

Neto, Paulo mendes de carvalho ^{[1
]}

Fehlberg Junior, Renato ^{[2
]}

机构：

[1] Univ Fed Santa Catarina, Dept Math, R Eng Agron Andrei Cristian Ferreira, Florianopolis, SC, Brazil

[2] Univ Espirito Santo, Dept Math, Ave Fernando Ferrari 514, Vitoria, ES, Brazil

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2022年

关键词：

Riemann-Liouville fractional integral; Bochner-Lebesgue space; operator theory; semigroup theory; WELL-POSEDNESS; EQUATIONS; TIME;

D O I：

10.3934/cpaa.2022118

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study the Riemann-Liouville fractional integral of order alpha > 0 as a linear operator from L-p(I, X) into itself, when 1 <= p <= infinity, I = [t(0), t(1)] (or I = [t(0), infinity)) and X is a Banach space. In particular, when I = [t(0), t(1)], we obtain necessary and sufficient conditions to ensure its compactness. We also prove that Riemann-Liouville fractional integral defines a C-0-semigroup but does not defines a uniformly continuous semigroup. We close this study by presenting lower and higher bounds to the norm of this operator.

引用

页码：3667 / 3700

页数：34

共 35 条

[1]

Abramowitz M., 1964, Handbook of mathematical functions with formulas, graphs, and mathematical tables, V9th, DOI DOI 10.2307/2282672

[2] A Parabolic Problem with a Fractional Time Derivative [J].

Allen, Mark ;

Caffarelli, Luis ;

Vasseur, Alexis .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2016, 221 (02) :603-630

[3]

[Anonymous], 1948, Functional analysis and semi-groups

[4]

[Anonymous], 1972, Realizability theory for continuous linear systems

[5]

[Anonymous], 2013, Monotone operators in Banach space and nonlinear partial differential equations

[6]

[Anonymous], 1977, American Mathematical Soc.

[7]

Arendt W, 2011, MG MATH, V96, pIX, DOI 10.1007/978-3-0348-0087-7

[8]

Brezis H, 2011, UNIVERSITEXT, P1

[9] NONLINEAR STOCHASTIC TIME-FRACTIONAL DIFFUSION EQUATIONS ON R: MOMENTS, HOLDER REGULARITY AND INTERMITTENCY [J].

Chen, Le .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2017, 369 (12) :8497-8535

[10] On the fractional version of Leibniz rule [J].

de Carvalho Neto, Paulo M. ;

Fehlberg Junior, Renato .

MATHEMATISCHE NACHRICHTEN, 2020, 293 (04) :670-700

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