Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2019; 56(6): 1423-1433

Online first article October 17, 2019      Printed November 30, 2019

https://doi.org/10.4134/BKMS.b180934

Copyright © The Korean Mathematical Society.

Riemann-Liouville fractional fundamental theorem of calculus and Riemann-Liouville fractional Polya type integral inequality and its extension to Choquet integral setting

George A. Anastassiou

University of Memphis

Abstract

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.

Keywords: fractional fundamental theorem, fractional Polya integral inequality, Riemann-Liouville fractional derivative, Choquet integral

MSC numbers: Primary 26A33, 26D10, 26D15