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## Calculus Books / Fractional Calculus Books

### Fractional Calculus Books

#### 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):

136Pages

#### Fractional Calculus Integral and Differential Equations of Fractional Order

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

Author(s):

56Pages

#### 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):

61Pages

#### 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.

Author(s):

59Pages

#### 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):

56Pages

#### 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):

96Pages