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.