Fractional Derivatives of Certain Generalized Hypergeometric Functions of Several Variables

The main object of the present paper is to derive a number of key formulas for the fractional derivatives of the multivariable H-function (which is defined by a multiple contour integral of Mellin-Barnes type). Each of these formulas can be shown to yield interesting new results for various classes of generalized hypergeometric functions of several variables. Some of these applications of the key formulas provide potentially useful generalizations of known results in the theory of fractional calculus.