Advances in Operator Theory and Inequalities

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.

Keywords: Fractional derivatives, Green's identities, Picone identity, Hardy inequalities, uncertainty principles