All the special functions are fractional differintegrals of elementary functions

In this survey we discuss a unified approach to the generalized hypergeometric functions based on a generalized fractional calculus developed in the monography by Kiryakova. This generalization of the classical theory of the operators of integration and differentiation of fractional order deals with integral (differintegral) operators involving Meijer's G- and Fox's H-functions as kernel functions. Their theory is fully developed and illustrated by various special cases and applications in different areas of the applicable analysis.

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