Physics of Fractal Operators [Paperback]

This text describes the statistcal behavior of complex systems and shows how the fractional calculus can be used to model the behavior. The discussion emphasizes physical phenomena whose evolution is best described using the fractional calculus, such as systems with long-range spatial interactions or long-time memory. The book gives general strategies for understanding wave propagation through random media, the nonlinear response of complex materials, and the fluctuations of heat transport in heterogeneous materials.This text describes the statistcal behavior of complex systems and shows how the fractional calculus can be used to model the behavior. The discussion emphasizes physical phenomena whose evolution is best described using the fractional calculus, such as systems with long-range spatial interactions or long-time memory. The book gives general strategies for understanding wave propagation through random media, the nonlinear response of complex materials, and the fluctuations of heat transport in heterogeneous materials.1. Non-differentiable Processes 2. Failure of Traditional Models. 3. Fractional Dynamics. 4. Fractional Fourier Transforms. 5. Fractional Laplace Transforms. 6. Fractional Randomness. 7. Fractional Rheology. 8. Fractional Stochastics. 9. The Ant in the Gurge Metaphor. 10. Appendices

From the reviews:

Have you ever wondered about whether one can define differential derivative of non integer order and how useful these fractal derivatives would be? If the answer is yes this is the book to look at. The book is written by physicists with a pragmatic audience in mind. It contains a very thorough and clearly written discussion of the mathematical foundation as well as the applications to important and interesting mathematical and physical problems. All the topics are very main stream and of great general relevance...

I am glad I got to know this book. I don't know yet whether fractal calculus wilC(