Fractional Calculus and Special Functions

Fractional Calculus and Special Functions

This note explains the following topics: historical notes and introduction to fractional calculus, The Liouville weyl fractional calculus, The riesz feller fractional calculus, The Riemann Liouville fractional calculus, The Grunwald letnikov fractional calculus, The mittag Leffler function, The wright functions.

Author(s): Francesco Mainardi, University of Bologna

64 Pages

Construction and Physical Application Of The Fractional Calculus

This book covers the following topics about Fractional Calculus: Elementary preliminaries, Grunwald’s construction, The Riemann-Liouville construction, Abel’s solution of the tautochrone problem, Heaviside’s solution of the diffusion equation, Application to the differention of fractal curves, Charge density on a needle, Eigenfunctions of derivative operators of integral/fractional order, Applications to analysis.

Author(s): Nicholas Wheeler, Reed College Physics Department

59 Pages

Fractional Calculus Integral and Differential Equations of Fractional Order

This lectures note introduces 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.

Author(s): Rudolf Gorenflo and Francesco Mainardi

56 Pages

Introduction to fractional calculus (PDF 96P)

Covered topics are: Historical origins of fractional calculus, Fractional integral according to Riemann-Liouville, Caputo fractional derivative, Riesz-Feller fractional derivative, Grunwal-Letnikov, Integral equations, Relaxation and oscillation equations, Fractional diffusion equation, A nonlinear fractional differential equation, Stochastic solution, Geometrical interpretation of fractional integration

Author(s): R. Vilela Mendes

96 Pages