Fractional Calculus and the Future of Science

Fractional Calculus and the Future of Science

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 sci...

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Bibliographic Details
Format: eBook
Language:English
Published: Basel MDPI - Multidisciplinary Digital Publishing Institute 2022
Subjects:
Mathematics and Science
Research and information: general
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
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