Positive solutions to fractional boundary-value problems with p-Laplacian on time scales

In this article, we consider the following boundary-value problem of nonlinear fractional differential equation with p-Laplacian operator: D-alpha (phi(p)(D(alpha)u(t))) = f (t,u(t)), t is an element of[0,1](T), u(0) = u(sigma(1)) = D(alpha)u(0) = D(alpha)u(sigma(1)) = 0, where 1 < alpha <= 2 is a real number, the time scale T is a nonempty closed subset of R. Da is the conformable fractional derivative on time scales, phi(p)(s) = vertical bar s vertical bar(p-2)s, p > 1, phi(-1)(p) = phi(q), 1/p + 1/q = 1, and f : [0, sigma(1)] x[0,+infinity) -> [0,+infinity) is continuous. By the use of the approach method and fixed-point theorems on cone, some existence and multiplicity results of positive solutions are acquired. Some examples are presented to illustrate the main results.