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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
56Pages
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
61Pages
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
59Pages
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
56Pages
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
96Pages
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
18Pages
This note covers the following topics: The Weyl fractional integral and the Mellin transform, Electrical circuits with fractance, Generalized voltage divider, Fractional calculus in viscoelasticity, Fractional order multipoles in electromagnetism.
Author(s): Lokenath Debnath
18Pages
