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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 
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 Definitions and Applications
The first chapter explains definition of fractional calculus. The second and third chapters, look at the Riemann-Liouville definitions of the fractional integral and derivative. The fourth chapter looks at some fractional differential equations with an emphasis on the Laplace transform of the fractional integral and derivative. The last chapter describes application problems—a mortgage problem and a decay-growth problem.
Author(s): Joseph M. Kimeu, Western Kentucky University
61 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 PagesAdvertisement
