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Riemann–Liouville Fractional Fundamental Theorem of Calculus and Riemann–Liouville Fractional Polya Integral Inequality and the Generalization to Choquet Integral Case

  • George A. AnastassiouEmail author
Chapter
Part of the Studies in Computational Intelligence book series (SCI, volume 886)

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. See also [2].

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Copyright information

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of MemphisMemphisUSA

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