Vectorial Prabhakar Hardy Type Generalized Fractional Inequalities under Convexity


Hardy inequality
Hilfer fractional calculus
Prabhakar fractional calculus
Generalized fractional calculus

How to Cite

Anastassiou, G. A. . (2022). Vectorial Prabhakar Hardy Type Generalized Fractional Inequalities under Convexity. Journal of Advances in Applied & Computational Mathematics, 8, 34–74.


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.


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