VALLÉE-POUSSIN THEOREM FOR KATUGAMPOLA FRACTIONAL FUNCTIONAL DIFFERENTIAL EQUATIONS

We propose Vallée-Poussin theorem in form of three equivalent assertions for Katugampola fractional functional differential equation. Choosing corresponding function, we obtain explicit test of negativity of Green’s function in form of algebraic inequality. We discuss particular cases of functional equation such as equations with deviation to illustrate application of our technique. Further, we demonstrate applications of Katugampola derivatives as it generalizes previous inequalities available in literature for Riemann–Liouville fractional boundary value problem and Hadamard fractional boundary value problem.