Extremal points for fractional boundary value problems

Abstract

This article is concerned with characterizing the first extremal point, b0, for a Riemann–Liouville fractional boundary value problem, Dα0+y + p(t)y = 0, 0 < t < b, y(0) = y′(0) = y″(b) = 0, 2 < α ≤ 3, by applying the theory of u0-positive operators with respect to a suitable cone in a Banach space. The key argument is that a mapping, which maps a linear, compact operator, depending on b to its spectral radius, is continuous and strictly increasing as a function of b. Furthermore, an application to a nonlinear case is given.