ABSTRACT
This chapter deals with fractional derivatives and fractional integrals and their basic properties. Several methods including the Laplace transform are discussed to introduce the Riemann-Liouville fractional integrals. Attention is given to the Weyl fractional integral and its properties. Finally, the fractional derivative is applied to solve the celebrated Abel integral equation. This is followed by brief comments on the Heaviside operational calculus and modern applications of fractional calculus to science and engineering. This chapter is based on two articles of Debnath (2003, 2004) and hence, the reader is referred to these articles for all references cited in this chapter.
