Balanced fractional opial inequalities

Here we present Lp, p > 1, fractional Opial type inequalities subject to high order boundary conditions. They involve the right and left Caputo, Riemann–Liouville fractional derivatives. These derivatives are blended together into the balanced Caputo, Riemann–Liouville, respectively, fractional derivative. This balanced fractional derivative is introduced here for the first time. We give applications to a special case.