Jacobi-type functions defined by fractional Bessel derivatives

For a class of even weight functions, generalizations of the classical Jacobi and Laguerre polynomials are defined via fractional Rodrigues' type formulas using the Bessel operators in the form (d(2)/dx(2))+((2 beta+1)/x)(d/dx). Their properties, including hypergeometric representation, differential recurrence relations and fractional boundary value problem, are investigated.