The special functions of fractional calculus as generalized fractional calculus operators of some basic functions

We propose a unified approach to the so-called Special Functions of Fractional Calculus (SFs of FC), recently enjoying increasing interest from both theoretical mathematicians and applied scientists. This is due to their role as solutions of fractional order differential and integral equations, as the better mathematical models of phenomena of various physical, engineering, automatization, chemical, biological, Earth science, economics etc. nature.Our approach is based on the use of Generalized Fractional Calculus (GFC) operators. Namely, we show that all the Wright generalized hypergeometric functions (W.ghf-s) Ψqp(z) can be represented as generalized fractional integrals, derivatives or differ-integrals of three basic simpler functions as cosq−p(z)cosq−p(z), exp(z)exp(z) and Ψ01(z) (reducible in particular to the elementary function zα(1−z)βzα(1−z)β, the Beta-distribution), depending on whether p