The main aim of this paper is to construct an extension of Appell’s hypergeometric functions by means of modified Beta functions . We give integral representations for these functions and obtain some relations for these functions and extended Gauss hypergeometric function via decomposition operators defined by Burchnall and Chaundy. Furthermore, we present some transformation formulas for the first and second kind of extended Appell’s hypergeometric functions. Also, we give some relations between the first kind of extended Appell’s hypergeometric functions, Whittaker, and Modified Bessel functions.
