Riemann-liouville分数阶微积分基本定理和Riemann-liouville分数阶多型积分不等式及其在choquet积分集上的推广

IF 0.6 4区数学 Q3 MATHEMATICS

Bulletin of the Korean Mathematical Society Pub Date : 2019-01-01 DOI:10.4134/BKMS.B180934

G. Anastassiou

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引用次数: 5

摘要

本文首次给出了不带初始条件的分数阶微积分的左、右Riemann-Liouville分数阶基本定理。然后利用广义的左右Riemann-Liouville分数阶导数，建立了一个Riemann-Liouville分数阶Polya型积分不等式。这里令人惊奇的事实是，我们不需要任何边界条件，如经典的Polya积分不等式所要求的。将Polya不等式推广到Choquet积分集。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

RIEMANN-LIOUVILLE FRACTIONAL FUNDAMENTAL THEOREM OF CALCULUS AND RIEMANN-LIOUVILLE FRACTIONAL POLYA TYPE INTEGRAL INEQUALITY AND ITS EXTENSION TO CHOQUET INTEGRAL SETTING

Here we present the right and left Riemann-Liouville fractional fundamental theorems of fractional calculus without any initial conditions for the first time. Then we establish a Riemann-Liouville fractional Polya type integral inequality with the help of generalised right and left Riemann-Liouville fractional derivatives. The amazing fact here is that we do not need any boundary conditions as the classical Polya integral inequality requires. We extend our Polya inequality to Choquet integral setting.

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来源期刊

Bulletin of the Korean Mathematical Society 数学-数学

CiteScore

0.80

自引率

20.00%

发文量

审稿时长

6 months

期刊介绍： This journal endeavors to publish significant research of broad interests in pure and applied mathematics. One volume is published each year, and each volume consists of six issues (January, March, May, July, September, November).