Hilfer Fractional Quantum Derivative and Boundary Value Problems - Phollakrit Wongsantisuk; Sotiris K. Ntouyas; Donny Passary; Jessada Tariboon (Mathematics, 2022)
In this paper, we introduce an extension of the Hilfer fractional derivative, the “Hilfer fractional quantum derivative”, and establish some of its properties. Then, we introduce and discuss initial and boundary value problems involving the Hilfer fractional quantum derivative. The existence of a unique solution of the considered problems is established via Banach’s contraction mapping principle. Examples illustrating the obtained results are also presented.