Fractional Calculus: Integral and Differential Equations of Fractional Order

Understand

We introduce the linear operators of fractional integration and fractional differentiation in the framework of the Riemann-Liouville fractional calculus.

• Particular attention is devoted to the technique of Laplace transforms for treating these operators in a way accessible to applied scientists, avoiding unproductive generalities and excessive mathematical rigor.
• By applying this technique we shall derive the analytical solutions of the most simple linear integral and differential equations of fractional order.
• We show the fundamental role of the Mittag-Leffler function, whose properties are reported in an ad hoc Appendix.