Multivariable Jacobi Polynomials via Fractional Calculus

In recent years, many works on the subject of fractional calculus contain interesting accounts of the theory and applications of fractional calculus operators in a number of areas of mathematical analysis ( such as ordinary and partial differential equations, integral equations, summation of series, etc.). The main object of this paper is to construct multivariable extension of Jacobi polynomials by means of fractional derivative operator and to give various generating functions for these polynomials by making use of fractional calculus. Furthermore, we derive various families of multilinear and multilateral generating functions. Some special cases of the results presented in this study are also indicated.