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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
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
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