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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 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 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