Fractional Order Thinking in Exploring the Frontiers of STEM

Fractional Order Thinking (FOT) is about solving today’s complex problems in the physical, social and life sciences using the tools of fractional order calculus (FOC). Very soon after Mandelbrot introduced the fractal paradigm into the scientific lexicon it was shown that the integer order calculus (IOC) could not describe the dynamics of fractal processes. A new kind of calculus was required to construct the equations of motion for fractal dynamic processes which turned out to be fractional order Hamiltonian equations (FOHEs). The FOHEs are one tool in the FOC toolbox which concerns how to apply the operators  of differentiation and integration of non-integer orders. Rejecting the fractional calculus is equivalent to saying there are no numbers between neighboring integers.

In this book series, we explore the core motivation of fractional calculus by first showing the “core motivation” of IOC invented by Newton and Leibnitz, the fundamental ideas of which can be traced back to the time of Heraclitus of Ephesus. Our ultimate message is that the “IOC” is driven by “the desire and the need” for the “quantification of changes” based on energy gradients in complex dynamic networks, whereas “FOC” is driven by “the desire and the need of understanding complexity” based on information gradients in those same networks. In science, technology, engineering, and mathematics (STEM), metaphorically speaking, there is plenty of room between the integers to enable the archiving of better than the best modelling, control performance, robustness, resilience, and even intelligence.

There is an increasing interest in fractional order dynamic systems (FODS) and controls in the recent research literature, not only because of their novelty but also due to their practical applications. But to accomplish all of this requires a new way of thinking, the Fractional Order Thinking (FOT) referred to above, which in turn must be preceded by a new STEM curriculum. This series will offer a unique platform to demonstrate such additional benefits in our improved understanding of complexity and stochastic dynamics via FOT.

This exciting book series features:

• A forum demonstrating the good consequences of using fractional order thinking (FOT).
• Fractional calculus concepts are presented in the context of complex systems characterization while assuming minimal background in math and physics.
• A broad audience including professionals across many fields, the general public and courses in colleges and even high schools.
• Wide STEM topics ranging from batteries to medicine with a writing style easy to follow.
• Short and inexpensive books of 120-150 pages main text that can be written and read in a reasonable amount of time.

Please contact us if you have an idea for a book for the series.