ABSTRACT
The origin of special functions, known also as mathematical functions and higher transcendental functions, can be traced back to several widespread areas such as mathematical physics, analytic number theory, applied mathematical sciences and other fields. On the other hand, in the current literature, there are remarkably extensive usages of the operators of fractional calculus (that is, fractional-order integrals and fractional-order derivatives) in the modeling and analysis of a significantly large variety of applied scientific and real-world problems in mathematical, physical, biological, engineering and statistical sciences, and also in other scientific disciplines. Here, in this book chapter, we present a brief introductory overview and survey of some of the recent developments in the theory of various extensively-studied special functions and their usages in fractional calculus and its applications.
