Definitions and Numerical Evaluations of Fractional Calculus

As previously noted, fractional calculus dates back to the days when Newton and Leibniz first invented traditional calculus. In the absence of a unified and widely accepted definitions, fractional calculus did not progress well in its early development. In this chapter, various definitions of fractional derivatives and integrals are presented. The numerical solutions of derivatives and integrals under Grünwald–Letnikov, Riemann–Liouville and Caputo fractional-order definitions are presented. The properties and geometric interpretations are explored.