Fractional Calculus: Models And Numerical Methods (Second Edition)

Models and Numerical Methods

Dumitru Baleanu, Kai Diethelm;Enrico Scalas;Juan J Trujillo;

• Publisher: WSPC
• Year: 2016
• ISBN:
  9789813140059
• Edition: 2
• Topic: Matematica
• Subtopic: Matematica applicata

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This book will give readers the possibility of finding very important mathematical tools for working with fractional models and solving fractional differential equations, such as a generalization of Stirling numbers in the framewo

Chapter 1

Preliminaries

This chapter is preliminary in character and contents. We give here the definitions and some properties of several fractional integrals and fractional derivatives of different types. Also we give the definition and properties of some special functions which will be used in this book.

More detailed information about the content of this chapter may be found, for example, in the works of Erdélyi et al. [226], Copson [161], Riesz [520], Doetsch [204], Sneddon [570], Zemanian [646], McBride [413], Samko et al. [542], Kiryakova [340], Podlubny [487], Butzer et al. [125–127], Kilbas et al. [335], Caponetto et al. [139], Diethelm [186], Mainardi [398], Monje et al. [438], Duarte Ortigueira [209] and Tarasov [588].

In general, the results we present in this chapter will be considered for “suitable functions”. Precise details can be found, e. g., in the above mentioned references.

First of all, let Ω = [a, b] (−∞ ≤ a < b ≤ ∞) be a finite or infinite interval of the real axis

. We denote by L_p(a, b) (1 ≤ p ≤ ∞) the set of those Lebesgue complex-valued measurable functions f on Ω...