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# Fractional Calculus Definitions and Applications

## Fractional Calculus Definitions and Applications

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.

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61 Pages
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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.

61 Pages

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.

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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

96 Pages

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

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.

18 Pages