Riemann-Liouville fractional fundamental theorem of calculus and Riemann-Liouville fractional Polya type integral inequality and its extension to Choquet integral setting
Bull. Korean Math. Soc. 2019 Vol. 56, No. 6, 1423-1433
https://doi.org/10.4134/BKMS.b180934
Published online November 30, 2019
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
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