It is with pleasure that the authors extend their gratitude to the National Aeronautics and Space Administration, Glenn Research Center for their long-term and continued support of our work in both fractional calculus and fractional trigonometry. While many people have helped us in many ways, we are deeply indebted to the managers that have supported our work, including Dr. Norman Wenger, Dr. Walter C. Merrill, Dr. Jih-Fen Lei, Dr. Gary T. Seng of NASA Glenn Research Center, and Dr. Alex DeAbreu of the University of Akron. Also from NASA Glenn Research Center, we are grateful to Dr. Ten-Huei Guo for his review of many of our papers, Mr. Robert C. Anderson for his help when the computers become balky, and Dr. John Lekki for his enlightening and helpful discussions on photon entanglement.
We are grateful to our editors at John Wiley & Sons, Susanne Steitz-Filler and Allison McGinniss, for their support and guidance through the publication process.
We are most appreciative of Dr. Mary V. Zeller from NASA Glenn Research Center, whose support and encouragement during the writing of this book were most helpful.
We would like to express our gratitude to Professor Rachid Malti of Bordeaux University whose work on stability of elementary transfer functions of the second kind provides an important contribution to Chapter 13. We are grateful to Professor Diego Dominici of New York State University at New Paltz for his helpful discussions on inverse functions.
We would like to thank in advance any kind readers who forward to us any suggestions for improvement or corrections in the book.
Finally, we must recognize the support and love of our wives Margaret Lorenzo and Karen Hartley and our children Mary (Lorenzo) Stafford, Ann (Lorenzo) Wahlay, James Lorenzo, Carol (Lorenzo) Palko, Margaret (Lorenzo) Strekal, and John Hartley who give meaning to our work.