Opial type \(L^{p}\)-inequalities for fractional derivatives (Q1607921)

The paper is a certain revision of the previous article of the first author [``General fractional Opial type inequalities'', Acta Appl. Math. 54, No. 3, 303-317 (1998; Zbl 0921.26010)]. In this paper the authors present several versions of the weighted Opial-type inequality, considering \(L_p\)-setting instead of \(C\)-setting for considered fractional derivatives. They also make a change of the method of the proof, basing themselves on a more natural idea of the index law instead of making use of the fractional Taylor formula.