Fractional opial inequalities for several functions with applications


A large variety of very general Lp (1 ≤ p ≤ ∞) form Opial type inequalities ([10]) is presented involving generalized fractional derivatives ([5], [8]) of several functions in different orders and powers. The above are based on a generalization of Taylor's formula for generalized fractional derivatives ([5]). From the established results derive several other particular results of special interest. Applications of some of these special inequalities are given in proving 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. Copyright 2005 Eudoxus Press, LLC.

Publication Title

Journal of Computational Analysis and Applications

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