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Introduction to Fractional Differential Equations

Part of the Nonlinear Systems and Complexity Book Series (volume 25)

DOI: 10.1007/978-3-030-00895-6

ISBN: 978-3-030-00894-9

Publisher: Springer International Publishing - Springer Journals

Oct 29, 2018

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Chapter 1Special Functions

Milici, Constantin; Drăgănescu, Gheorghe; Tenreiro Machado, J.

Pages: 1 –15

[In this chapter several special functions used in the follow-up of the book are presented briefly.]
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Chapter 2Fractional Derivative and Fractional Integral

Milici, Constantin; Drăgănescu, Gheorghe; Tenreiro Machado, J.

Pages: 17 –31

[For every α > 0 and a local integrable function f(t), Right fractional integral the right FI of order α is defined: aItαf(t)=1Γ(α)∫at(t−u)α−1f(u)du,−∞≤a

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Chapter 3The Laplace Transform

Milici, Constantin; Drăgănescu, Gheorghe; Tenreiro Machado, J.

Pages: 33 –46

[A function f(t) is called original function if: f(t) ≡ 0 for t < 0,|f(t)|

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Chapter 4Fractional Differential Equations

Milici, Constantin; Drăgănescu, Gheorghe; Tenreiro Machado, J.

Pages: 47 –86

[Let the fractional differential equation (FDE) be (Da+αy)(t)=f[t,y(t)],α>0,t>a,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}...
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Chapter 5Generalized Systems

Milici, Constantin; Drăgănescu, Gheorghe; Tenreiro Machado, J.

Pages: 87 –120

[This chapter addresses the generalization of classical models and systems in the perspective of FC. The following sections study the Cornu, Emden, Hermite, Legendre, and Bessel fractional systems.]
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Chapter 6Numerical Methods

Milici, Constantin; Drăgănescu, Gheorghe; Tenreiro Machado, J.

Pages: 121 –185

[This chapter studies several numerical methods for fractional order systems. In the following sections variational iteration, least squares, Euler’s, and Runge–Kutta methods are analyzed.]

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