Certain Fractional Derivative Formulae Involving the Product of a General Class of Polynomials and the Multivariable Gimel-Function (Global Journal of Science Frontier Research, 2018)
In the present paper, we obtain three unified fractional derivative formulae. The first involves the product of a general class of polynomials and the multivariable Gimel-function. The second involves the product of a general class of polynomials and two multivariable Gimel-functions and has been obtained with the help of the generalized Leibniz rule for fractional derivatives. The last fractional derivative formulae also involves the product of a general class of polynomials and the multivariable Gimel-function but it is obtained by the application of the first fractional derivative formulae twice and, it involve two independents variables instead of one. The polynomials and the functions involved in all our fractional derivative formulae as well as their arguments which are of the type. The formulae are the very general character and thus making them useful in applications. In the end, we shall give a particular case.
Keywords: multivariable gimel-function; riemann-liouville and erdélyi-kober fractional operators; general class of polynomials; fractional derivative formulae