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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 Books
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Fractional Calculus Integral and Differential Equations of Fractional Order

PDF | 56 Pages | English
This note covers the following topics: Introduction To Fractional Calculus, Fractional Integral Equations, Fractional Differential Equations and The Mittag-leffler Type Functions.

 
Fractional Calculus Definitions and Applications

PDF | 61 Pages | English
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 Calculus

PDF | 59 Pages | English
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 Order

PDF | 56 Pages | English
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)

PDF | 96 Pages | English
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)

PDF | 28 Pages | English
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)

PDF | 18 Pages | English
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.

 
Recent Application of Fractional Calculus to Science and Engineering (PDF 31P)

PDF | 18 Pages | English
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.

 
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