Download An Introduction to the Fractional Calculus and Fractional by Kenneth S. Miller PDF

By Kenneth S. Miller

Commences with the old improvement of fractional calculus, its mathematical theory—particularly the Riemann-Liouville model. a variety of examples and theoretical functions of the idea are awarded. gains themes linked to fractional differential equations. Discusses Weyl fractional calculus and a few of its makes use of. contains chosen actual difficulties which result in fractional differential or imperative equations.

Show description

Read or Download An Introduction to the Fractional Calculus and Fractional Differential Equations PDF

Similar calculus books

A Primer on Integral Equations of the First Kind: The Problem of Deconvolution and Unfolding

I used to be a bit upset through this publication. I had anticipated either descriptions and a few useful aid with the way to clear up (or "resolve", because the writer prefers to assert) Fredholm vital equations of the 1st style (IFK). as a substitute, the writer devotes approximately a hundred% of his efforts to describing IFK's, why they're tricky to accommodate, and why they can not be solved by way of any "naive" tools.

Treatise on Analysis,

This quantity, the 8th out of 9, maintains the interpretation of "Treatise on research" by means of the French writer and mathematician, Jean Dieudonne. the writer indicates how, for a voluntary constrained category of linear partial differential equations, using Lax/Maslov operators and pseudodifferential operators, mixed with the spectral concept of operators in Hilbert areas, ends up in options which are even more specific than ideas arrived at via "a priori" inequalities, that are dead functions.

Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra

An creation to the Calculus, with a great stability among thought and strategy. Integration is handled sooner than differentiation--this is a departure from latest texts, however it is traditionally right, and it's the most sensible method to determine the real connection among the crucial and the by-product.

Additional resources for An Introduction to the Fractional Calculus and Fractional Differential Equations

Example text

As we go on, the methods of approximation will become more involved. Let us take a look at some crude ones. We will approximate in three ways. Example 33— Approximate this integral with three equal subdivisions, using the right end of each one. Here's the picture: The approximate area is f(w1)∆x1 + f(w2)∆x2 + f(w3)∆x3. Each ∆x = 2, and W1 = 1, w2 = 3, and w3 = 5, the right ends of each interval. The approximation is (∆x)[f(1) + f(3) + f(5)] = 2(3 + 11 + 27) = 82. Example 34— Same picture, same intervals, the minimum approximation, the smallest value in each interval, S 3.

Which rectangular beam that can be cut from a circular log of radius 10 inches will have maximum strength? If we let x be the width and y be the depth, we can write the equation without a picture. The strength S = kxy 2 ; k is an unknown constant. To find a relationship between x and y, we need a picture of the log. One of the things we always look for is the Pythagorean relationship. In this case x2 + y2 = 400 (the square of the diameter). In the original equation, it is easier to solve for y 2, because if we solved for x we would have a square root, which would make the derivative much more difficult and sometimes impossible to finish.

Oblique (Slanted Line) Asymptote This occurs when the degree of the top is exactly 1 more than the bottom. Example 10— Degree of the top = 2; degree of the bottom = 1. Oblique asymptote. We must, unfortunately, long divide the bottom into the top. If you know it, use synthetic division. As x goes to infinity, the remainder 21/(x + 4) goes to 0. The oblique asymptote is y = x - 6. Note 1 If the degree of the top is more than the bottom but not 1, there are no oblique asymptotes. Note 2 At most there is one oblique asymptote or one horizontal asymptote, but not both.

Download PDF sample

Rated 4.60 of 5 – based on 25 votes