Canavati Fractional Opial–Type Inequalities for Several Functions and Applications

A wide variety of very general L _p (1 ≤ p ≤ ∞)-form Opial-type inequalities [315] is presented involving generalized Canavati fractional derivatives [17, 101] of several functions in different orders and powers. The above are based on a generalization of Taylor–s formula for generalized Canavati fractional derivatives [17]. From the established results are derived several other particular results of special interest. Applications of some of these special inequalities are given in proving the uniqueness of solution and in giving upper bounds to solutions of initial value problems involving a very general system of several fractional differential equations. Upper bounds to various fractional derivatives of the solutions that are involved in the above systems are given too. This treatment is based on [27].