Vallée-Poussin theorem for Hadamard fractional functional differential equations

We propose necessary and sufficient conditions for the negativity of the two-point boundary value problem in the form of the Vallée-Poussin theorem about differential inequalities for the Hadamard fractional functional differential problem (Formula presented.) Here, the operator (Formula presented.) can be an operator with deviation (of delayed or advanced type), an integral operator or various linear combinations and superpositions. For example, the operator can be of the forms (Formula presented.), (Formula presented.) or (Formula presented.). We obtain explicit tests of negativity of Green's function in the form of algebraic inequalities. Our paper is the first one where a general form of the operator is considered with Hadamard fractional derivatives.