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We introduce the linear operators of fractional integration and fractionaldifferentiation in the framework of the Riemann-Liouville fractional calculus.Particular attention is devoted to the technique of Laplace transforms fortreating these operators in a way accessible to applied scientists, avoidingunproductive generalities and excessive mathematical rigor. By applying thistechnique we shall derive the analytical solutions of the most simple linearintegral and differential equations of fractional order. We show thefundamental role of the Mittag-Leffler function, whose properties are reportedin an ad hoc Appendix. The topics discussed here will be: (a) essentials ofRiemann-Liouville fractional calculus with basic formulas of Laplacetransforms, (b) Abel type integral equations of first and second kind, (c)relaxation and oscillation type differential equations of fractional order.

Fractional Calculus: Integral and Differential Equations of Fractional Order