Construction and Physical Application Of The Fractional Calculus
Construction and Physical Application Of The Fractional Calculus
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): Nicholas Wheeler,
Reed College Physics Department
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): Ricardo Almeida, Dina Tavares, Delfim F. M.
Torres
This note covers the following topics:
Introduction To Fractional Calculus, Fractional Integral Equations, Fractional
Differential Equations and The Mittag-leffler Type Functions.
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): Joseph M. Kimeu, Western
Kentucky University