Fractional Calculus and the Future of Science 

 - Basel  MDPI - Multidisciplinary Digital Publishing Institute  2022 
 - 1 online resource (312 p.) 
<br/><br/> Open Access 
<br/><br/> Newton foresaw the limitations of geometry's description of planetary behavior and developed fluxions (differentials) as the new language for celestial mechanics and as the way to implement his laws of mechanics.  Two hundred years later Mandelbrot introduced the notion of fractals into the scientific lexicon of geometry, dynamics, and statistics and in so doing suggested ways to see beyond the limitations of Newton's laws. Mandelbrot's mathematical essays suggest how fractals may lead to the understanding of turbulence, viscoelasticity, and ultimately to end of dominance of the Newton's macroscopic world view.Fractional Calculus and the Future of Science examines the nexus of these two game-changing contributions to our scientific understanding of the world. It addresses how non-integer differential equations replace Newton's laws to describe the many guises of complexity, most of which lay beyond Newton's experience, and many had even eluded Mandelbrot's powerful intuition. The book's authors look behind the mathematics and examine what must be true about a phenomenon's behavior to justify the replacement of an integer-order with a noninteger-order (fractional) derivative. This window into the future of specific science disciplines using the fractional calculus lens suggests how what is seen entails a difference in scientific thinking and understanding. 
<br/><br/><br/>Creative Commons 
<br/><br/><br/>English 
<br/><br/><label>ISBN: </label>9783036528267 9783036528274 books978-3-0365-2827-4 
<br/><br/><label>Standard No.: </label>10.3390/books978-3-0365-2827-4  doi 
<br/><br/><label>Subjects--Topical Terms: </label><br/>Mathematics and Science<br/>Research and information: general
<br/><br/><label>Subjects--Index Terms: </label>big data chaos complex systems complexity continuous time random walk continuous time random walks control theory diffusion-wave equation distributed-order operators diversity Dow Jones entropy false positive rate financial indices fractals fractional calculus fractional conservations laws fractional diffusion fractional dynamics fractional order PID control fractional PINN fractional Poisson process complex systems fractional relaxation fractional telegrapher's equation fractional-order thinking frequency-domain control design Gaussian watermarks heavytailedness Laplace and Fourier transform Lévy measure liouville-caputo fractional derivative local discontinuous Galerkin methods logistic differential equation machine learning Mittag-Leffler functions multidimensional scaling n/a optimal tuning physics-informed learning PMSM Poisson process of order k reaction kinetics reaction-diffusion equations running average semi-fragile watermarking system Skellam process stability estimate statistical assessment subordination telegrapher's equations transport problems transport processes turbulent flows variability variable fractional model viscoelasticity Wright functions