Operational Representation of Certain Hypergeometric Functions by Means of Fractional Derivatives and Integrals

The investigation in the present paper is to obtain certain types of relations for the well known hypergeometric functions by employing the technique of fractional derivative and integral. Mathematics Subject Classification(2010): Primary 42C05, Secondary 33C20, 26A33. Keywords—Fractional Derivatives and Integrals, Hypergeometric functions. THE names fractional calculus is concerned with the generalization of differentiation and integration to fractional order. There are number of ways of defining fractional derivatives and integrals. We begin by recalling S.F. Lacroix [9] definition of mth derivatives for y = x, where n is a positive integer as dy dxn = (m!) (n−m)! n−m (1) A vital development in the field of fractional calculus was laid down by L. Euler, N.H. Abel, J. Liouville, and B. Riemann. For the function f(x), expanded in series form