Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation:
Fractional Calculus and Applied Analysis, Vol. 8, No 4, (2005), 431p-438p
Abstract:
This paper refers to a fractional order generalization of the classical Jacobi
polynomials. Rodrigues’ type representation formula of fractional order
is considered. By means of the Riemann–Liouville operator of fractional
calculus fractional Jacobi functions are defined, some of their properties are
given and compared with the corresponding properties of the classical
Jacobi polynomials. These functions appear as a special case of a fractional
Gauss function, defined as a solution of the fractional generalization of the
Gauss hypergeometric equation.