TY  - BOOK
TI  - Fractional Calculus and the Future of Science
SN  - 9783036528267
PY  - 2022///
CY  - Basel
PB  - MDPI - Multidisciplinary Digital Publishing Institute
KW  - Mathematics and Science
KW  - bicssc
KW  - Research and information: general
KW  - big data
KW  - chaos
KW  - complex systems
KW  - complexity
KW  - continuous time random walk
KW  - continuous time random walks
KW  - control theory
KW  - diffusion-wave equation
KW  - distributed-order operators
KW  - diversity
KW  - Dow Jones
KW  - entropy
KW  - false positive rate
KW  - financial indices
KW  - fractals
KW  - fractional calculus
KW  - fractional conservations laws
KW  - fractional diffusion
KW  - fractional dynamics
KW  - fractional order PID control
KW  - fractional PINN
KW  - fractional Poisson process complex systems
KW  - fractional relaxation
KW  - fractional telegrapher's equation
KW  - fractional-order thinking
KW  - frequency-domain control design
KW  - Gaussian watermarks
KW  - heavytailedness
KW  - Laplace and Fourier transform
KW  - Lévy measure
KW  - liouville-caputo fractional derivative
KW  - local discontinuous Galerkin methods
KW  - logistic differential equation
KW  - machine learning
KW  - Mittag-Leffler functions
KW  - multidimensional scaling
KW  - n/a
KW  - optimal tuning
KW  - physics-informed learning
KW  - PMSM
KW  - Poisson process of order k
KW  - reaction kinetics
KW  - reaction-diffusion equations
KW  - running average
KW  - semi-fragile watermarking system
KW  - Skellam process
KW  - stability estimate
KW  - statistical assessment
KW  - subordination
KW  - telegrapher's equations
KW  - transport problems
KW  - transport processes
KW  - turbulent flows
KW  - variability
KW  - variable fractional model
KW  - viscoelasticity
KW  - Wright functions
N1  - Open Access
N2  - 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
UR  - https://directory.doabooks.org/handle/20.500.12854/81009
UR  - https://mdpi.com/books/pdfview/book/5351
ER  -