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http://dx.doi.org/10.4134/BKMS.b180934

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

Anastassiou, George A. (Department of Mathematical Sciences University of Memphis)

Publication Information

Bulletin of the Korean Mathematical Society / v.56, no.6, 2019 , pp. 1423-1433 More about this Journal

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;

Citations & Related Records

Reference

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