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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.

Author(s): 61 Pages Similar Books

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. 56 Pages

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. 56 Pages

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