Anisotropic Hardy type inequalities with weights and conformable fractional differential operators

TL;DR

This paper develops new anisotropic Hardy inequalities involving weights and conformable fractional derivatives, extending classical inequalities and deriving related uncertainty principles through advanced calculus tools.

Contribution

It introduces a systematic framework for conformable calculus, establishing divergence theorem, Green's identities, and anisotropic Hardy inequalities with weights and fractional operators.

Findings

Derived generalized anisotropic Hardy inequalities with weights.

Established new Heisenberg-Pauli-Weyl uncertainty principles.

Extended classical inequalities using conformable fractional calculus.

Abstract

By a systematic development of fundamental concepts of conformable calculus we establish conformable divergence theorem and Green's identities which we combine with some new anisotropic Picone type identities to derive a generalized anisotropic Hardy type inequality with weights and conformable fractional differential operators. As a consequence, several Hardy type inequalities and Heisenberg Pauli-Weyl uncertainty principles are obtained.