A new Picone’s dynamic inequality on time scales with applications

In this paper, we will derive a new dynamic Picone-type inequality for half-linear dynamic equations and dynamic inequalities of second order on an arbitrary time scale TT. As a consequence, we will apply this new Picone inequality to get a new Wirtinger-type inequality on time scales with two different weighted functions. The results contain the Wirtinger inequalities formulated by Beesack, Lee and Jaroš for the continuous case. For the discrete case our results are also new.