This section contains free e-books and guides on Fractional Calculus, some of the resources in this section can be viewed online and some of them can be downloaded.
Fractional Calculus Definitions and ApplicationsJoseph M. Kimeu, Western
| 61 Pages
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.
Construction and Physical Application Of The Fractional CalculusNicholas Wheeler,
Reed College Physics DepartmentPDF
| 59 Pages
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.
Fractional Calculus Integral and Differential Equations of Fractional OrderRudolf
Gorenflo and Francesco MainardiPDF
| 56 Pages
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.
Introduction to fractional calculus (PDF 96P)R. Vilela MendesPDF
| 96 Pages
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
Fractional Calculus History, Definitions and Applications for the Engineer (PDF 28P)Adam LoverroPDF
| 28 Pages
This note is aimed at the engineering or scientific
professional who wishes to learn about Fractional Calculus and its possible
applications in his/her field of study. The intent is to expose the reader to
the concepts, applicable definitions, and execution of fractional calculus and
second to show how these may be used to solve several modern problem.
Fractional calculus basic theory and applications (PDF 18P)Diego
| 18 Pages
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.