A bibliography on the numerical solution of delay differential equations

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THEORY AND APPLICATIONS

OF FRACTIONAL DIFFERENTIAL

EQUATIONS

ANATOLYA. KILBAS

Belarusian State University

Minsk, Belarus

HARI M. SRIVASTAVA

University of Victoria

Victoria, British Columbia, Canada

JUAN J. TRUJILLO

Universidad de La Laguna

La Laguna (Tenerife)

Canary Islands, Spain

ELSEVIER

Amsterdam - Boston - Heidelberg - London - New York - Oxford

Paris - San Diego - San Francisco - Singapore - Sydney - Tokyo

Contents

1 PRELIMINARIES 1

1.1 Spaces of Integrable, Absolutely Continuous, and Continuous Func-

tions ' 1

1.2 Generalized Functions 6

1.3 Fourier Transforms 10

1.4 Laplace and Mellin Transforms 18

1.5 The Gamma Function and Related Special Functions 24

1.6 Hypergeometric Functions 27

1.7 Bessel Functions 32

1.8 Classical Mittag-Leffler Functions 40

1.9 Generalized Mittag-Leffler Functions 45

1.10 Functions of the Mittag-Leffler Type 49

Getting started

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Technicalnote:CurvefittingwiththeREnvironmentforStatisticalComputing

DGRossiter

DepartmentofEarthSystemsAnalysis

InternationalInstituteforGeo-informationScience&EarthObservation

(ITC)

Enschede(NL)

December15,2009

Contents

1Curvefitting1

2Fittingintrinsicallylinearrelations1

3Fittinglinearizablerelations1

4Non-linearcurvefitting2

4.1Fittingapowermodel.......................2

4.2Fittingtoafunctionalform....................4

4.3Fittinganexponentialmodel...................6

4.4Fittingapiecewisemodel.....................8

References13

IndexofRconcepts14

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