This book is a landmark title in the continuous move from integer to non-integer in mathematics: from integer numbers to real numbers, from factorials to the gamma function, from integer-order models to models of an arbitrary order. For historical reasons, the word 'fractional' is used instead of the word 'arbitrary'.

All of us have read about the vast potential inherent in nanotechnology and the exciting impact it has had in changing our lifestyle in the 21st century. One of the basic issues confronting us is how to fabricate devices or materials on the nano scale. What is the basic physics governing the formation of nano phases? How can biological systems inspire us to formulate nano scale architectures, in the way nature has always done and continues to do? These are two main areas of focus in this book.

This volume provides a posteriori error analysis for mathematical idealizations in modeling boundary value problems, especially those arising in mechanical applications, and for numerical approximations of numerous nonlinear variational problems. The author avoids giving the results in the most general, abstract form so that it is easier for the reader to understand more clearly the essential ideas involved. Many examples are included to show the usefulness of the derived error estimates.

The dentate gyrus is a part of the brain that has been a topic of intense interest since the beginning of neuroscience, and pioneering studies from the distant and recent past attest to this. One of the reasons for such interest is that this structure provides some of the most remarkable examples of plasticity within the nervous system. In addition, it is critical to normal cognitive function, although exactly how and when is still a question that eludes answers. Furthermore, abnormalities within the dentate gyrus appear to play a role in diverse clinical conditions, from depression to epilepsy and traumatic brain injury. The primary goal of this book is to provide a context, or background, upon which the detailed knowledge of the current era can be appreciated. A series of overviews are provided to clarify essentials related to structural organization and development, cellular components, neurotransmitters and neuromodulators, plasticity, and clinical relevance.