Criteria of Existence for a q Fractional p-Laplacian Boundary Value Problem - Ragoub, Lakhdar; Tchier, Fairouz; Tawfiq, Ferdous (Frontiers in Applied Mathematics and Statistics, 2020)
This paper is devoted to establish Lyapunov-type inequalities for a class of fractional q-difference boundary value problem involving p-Laplace operator. Also, it is worth to mention that the Hartman-Wintner inequality for the qfractional p-Laplace boundary value problem is provided. The non existence of non trivial of solutions to the q-difference fractional p-Laplace equation subject to the Riemann-Liouville mixed boundary conditions will obey such integral inequalities. The tools mainly rely on a construction of a Green function corresponding to the considered problem, and its properties as well as its maximum value. In order to illustrate this result, we provide an interval where an appropriate Mittag-Leffler function to the given eigenvalue fractional boundary problem has no real zeros.