Mathematical Physics Vol 1

VI

Fractional Calculus

8

Introduction to the Fractional Calcu lus ................................. 435 8.1 Brief History of Fractional Calculus 8.2 Basic Definitions of Frac tional Order Differintegrals 8.3 Basic Properties of Fractional Order Differintegrals 8.4 Some other types of fractional derivatives

Appendices ........................ 453

A

Appendix Fractional Calculus: A Survey of Useful Formulas .................. 455

A.1 Introduction A.2 Notation and Special Functions A.3 Fractional Derivatives and Integrals A.4 Analytical Expressions of Some Fractional Derivatives

A.5 Laplace and Fourier Transforms A.6 Systems of Fractional Equations A.7 Transfer Functions A.8 An Introduction to Fractional Vector Operators

Bibliography ....................... 473

Index ................................. 479