Abstract
AbstractWe give here \(\psi \)-Hilfer and Hilfer fractional self adjoint operator inner product comparison, Poincaré, Sobolev and Opial type inequalities. At first we give right and left \(\psi \)-Hilfer fractional representation formulae in the self adjoint operator sense. Operator inequalities are based in the self adjoint operator order over a Hilbert space. It follows [3].
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