| | | Preface | | |
| Ch. I | | An Introduction to Fractional Calculus by P. L. Butzer and U. Westphal | | 1 |
| Ch. II | | Fractional Time Evolution by R. Hilfer | | 87 |
| Ch. III | | Fractional Powers of Infinitesimal Generators of Semigroups by U. Westphal | | 131 |
| Ch. IV | | Fractional Differences, Derivatives and Fractal Time Series by B. J. West and P. Grigolini | | 171 |
| Ch. V | | Fractional Kinetics of Hamiltonian Chaotic Systems by G. M. Zaslavsky | | 203 |
| Ch. VI | | Polymer Science Applications of Path-Integration, Integral Equations, and Fractional Calculus by J. F. Douglas | | 241 |
| Ch. VII | | Applications to Problems in Polymer Physics and Rheology by H. Schiessel and Chr. Friedrich and A. Blumen | | 331 |
| Ch. VIII | | Applications of Fractional Calculus Techniques to Problems in Biophysics by T. F. Nonnenmacher and R. Metzler | | 377 |
| Ch. IX | | Fractional Calculus and Regular Variation in Thermodynamics by R. Hilfer | | 429 |