This survey intends to report some of the major documents and events in the area of frac-tional calculus that took place since 1974 up to the present date.

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a b s t r a c tThis paper is a short description of our recent results on an important class of the so-called ''Special Functions of Fractional Calculus'' (SF of FC), which became important as solutions of fractional order (or multi-order) differential and integral equations, control systems and refined mathematical models of various physical, chemical, economical, management, bioengineering phenomena. Basically, under ''SF of FC'' we mean the Wright generalized hypergeometric function p Ψ q , as a special case of the Fox H-function. We have introduced and studied the multi-index Mittag-Leffler functions as their typical representatives, including many interesting special cases that have already proven their usefulness in FC and its applications. Some new results are also presented and open problems are discussed.

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In the last decades fractional calculus (FC) became an area of intensive research and development. This paper goes back and recalls important pioneers that started to apply FC to scientific and engineering problems during the nineteenth and twentieth centuries. Those we present are, in alphabetical order:

Since the 60s of last century Fractional Calculus exhibited a remarkable progress and presently it is recognized to be an important topic in the scientific arena. This survey analyzes and measures the evolution that occurred during the last five decades in the light of books, journals and conferences dedicated to the theory and applications of this mathematical tool, dealing with operations of integration and differentiation of arbitrary (fractional) order and their generalizations.MSC 2010 : Primary 26A33; 01A60, 01A61, 01A67; Secondary 34A08, 35R11, 60G22Key Words and Phrases: fractional calculus, development, fractional order differential equations, fractional order mathematical models, applications 1. IntroductionFractional Calculus (FC) started with the ideas of Gottfried Leibniz by the end of the XVII century and had been developed progressively up to now. During the recent decades FC, as an extension of the classical Calculus, attracted the attention of many researchers in several areas, namely mathematics, physics, engineering, biology, finance, economy, chemistry and social sciences. The reason is that the differential and integral equations and dynamical systems of fractional order can model mathematically the phenomena of Nature and Society more adequately than these restricted to integer order.