Open AccessVectorial Prabhakar Hardy Type Generalized Fractional Inequalities under Convexity
Author(s) -
George A. Anastassiou
Publication year - 2022
Publication title -
journal of advances in applied and computational mathematics
Language(s) - English
Resource type - Journals
ISSN - 2409-5761
DOI - 10.15377/2409-5761.2021.08.4
Subject(s) - convexity , mathematics , type (biology) , norm (philosophy) , fractional calculus , inequality , pure mathematics , mathematical analysis , finance , ecology , political science , law , economics , biology
We present a detailed great variety of Hardy type fractional inequalities under convexity and Lp norm in the setting of generalized Prabhakar and Hilfer fractional calculi of left and right integrals and derivatives. The radial multivariate case of the above over a spherical shell is developed in detail to all directions. Many inequalities are of vectorial splitting rational Lp type or of separating rational Lp type, others involve ratios of functions and of fractional integral operators.