Opial type inequalities involvingfractional derivatives of two functions and applications

A large variety of very general, but basic Lp (1 < p < ∞) form, Opial type inequalities [1] is established involving generalized fractional derivatives [2,3] of two functions in different orders and powers. The above rely on a generalization of Taylorʹs formula for generalized fractional derivatives [2]. From the developed results derive several other concrete results of special interest. The sharpness of inequalities is established there. Finally, applications of some of these special inequalities are given in establishing uniqueness of solution and in giving upper bounds to solutions of initial value problems involving a very general system of two fractional differential equations. Also, upper bounds to various fractional derivatives of the solutions that are involved in the above systems are presented.