This book is not a text devoted to a pedagogical presentation of a specialized topic nor is it a monograph focused on the author's area of research. It accomplishes both these things while providing a rationale for why the reader ought to be interested in learning about fractional calculus. This book is for researchers who has heard about many of these scientifically exotic activities, but could not see how they fit into their own scientific interests, or how they could be made compatible with the way they understand science. It is also for beginners who have not yet decided where their scientific talents could be most productively applied. The book provides insight into the long-term direction of science and show how to develop the skills necessary to successfully do research in the twenty-first century.

This book explains the quantitative reasoning required by the fractional calculus applied to complex physical, social, and biological phenomena. Fractional calculus is inextricably linked to complexity and provides a way to think systematically about complex phenomena without restricting it to a particular discipline. The book presents the case for science moving away from the fragmented disciplinary constructs devised to make the understanding of complex phenomena intellectually manageable, thus regaining its integrated nature as "natural philosophy" and underscoring how fractional calculus is the vehicle for accomplishing this task.