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Fractional calculus basic theory and applications (PDF 18P)
This note covers the following topics: Applications to transport in fusion plasmas, Riemann Liouville derivatives, Caputo fractional derivative, Local and non local transport, Application to reaction diffusion systems, Asymmetric front dynamics.
Author(s): Diego del-Castillo-Negrete
18 Pages 
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
The Variable Order Fractional Calculus of Variations
Fractional calculus is a recent field of mathematical analysis and it is a generalization of integer differential calculus, involving derivatives and integrals of real or complex order. This PDF book covers the following topics related to Fractional Calculus : Fractional calculus, The calculus of variations, Expansion formulas for fractional derivatives, The fractional calculus of variations.
Author(s): Ricardo Almeida, Dina Tavares, Delfim F. M. Torres
136 Pages
Fractional Calculus Integral and Differential Equations of Fractional Order
This note covers the following topics: Introduction To Fractional Calculus, Fractional Integral Equations, Fractional Differential Equations and The Mittag-leffler Type Functions.
Author(s): Rudolf Gorenflo and Francesco Mainardi
56 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