Riemann–Liouville Fractional Fundamental Theorem of Calculus and Riemann–Liouville Fractional Polya Integral Inequality and the Generalization to Choquet Integral Case
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.G.A. Anastassiou, Riemann-Liouville fractional fundamental theorem of Calculus and Riemann-Liouville Fractional Polya type integral inequality and its extension to Choquet integral setting, Bulletin of Korean Mathematical Society (2019)Google Scholar
- 9.G. Polya, G. Szegö, Problems and Theorems in Analysis, vol. I, Chinese edn (1984)Google Scholar
- 10.F. Qi, Polya type integral inequalities: origin, variants, proofs, refinements, generalizations, equivalences, and applications. RGMIA, Res. Rep. Coll., article no. 20, vol. 16 (2013). http://rgmia.org/v16.php