INDEX

#

20th century, 96, 123

A

abstraction, 53 accelerometers, 69 acrylonitrile, 200 action potential, 247 actuation, 56

actuators, 150, 154, 161

adaptation, 20, 149, 153, 154, 156, 254 aggregation, 16, 19

Algeria, 65

algorithm, 25, 34, 59, 67, 76, 79, 83, 85, 88, 149, 150, 151, 161, 254, 259, 260, 261, 268, 271, 273, 274, 275, 279, 284, 285, 286, 287, 288

amplitude, 42, 57, 68, 126, 127, 128, 132, 139, 140, 142, 143, 182, 192, 216, 218, 262, 271

analgesic, 247 anatomy, 256

anesthesiologist, 243, 252 anomalous diffusion, 240 assimilation, 244 asthmatic children, 147 asymmetry, 203

auditory evoked potentials, 257 Austria, 288

automation, 66

automotive applications, 45, 61

B

bandwidth, 49, 50, 51, 52

base, 2, 263, 265, 266, 267, 270, 271, 274, 284 batteries, 2, 4, 16

beams, 165

behaviors, 50, 98, 101, 111, 112, 113, 114, 115 Belgium, viii, 243

benefits, 38, 39, 40, 48, 52, 57

bisphenol, 200 blood pressure, 252 bounds, 17

brain, 247 branching, 11 breathing, 256

Brownian motion, 230 Bulgaria, viii

C

calculus, viii, ix, 15, 20, 38, 39, 61, 65, 66, 88, 89, 96, 120, 149, 150, 151, 162, 166, 167, 168, 169, 171, 198, 199, 200, 201, 203, 204, 205, 207, 209, 220, 221, 222, 223, 224, 227, 229, 243, 246, 247, 255, 257, 259, 286, 287, 288

Caputo derivative, 151, 166 cardiac output, 252

Cauchy problem, 235, 236, 239, 241 causality, 7, 9

CDC, 90, 256

chaos, ix, 16, 19, 21, 23, 29, 30, 32, 34, 257 chemical, 158, 161, 246

Chicago, 226 China, viii

closure, 7, 16, 18, 55 combustion, 58, 61 community, viii, 2, 247 compatibility, 19, 211 compensation, 49 competition, 16, 18, 274

complex non-integer orders, vii complex numbers, 3 complexity, 46, 48, 69, 130 compliance, 181, 182, 183, 191 composites, 225 compressibility, 39 compression, 165

computation, 3, 76, 79, 262, 267 computing, 53, 134

conduction, 94, 106, 119, 120, 147, 227, 228, 229, 230, 232, 239, 240, 241

conductivity, 94, 106, 124, 125

configuration, 273 conscious awareness, 247 conservation, 227 constant load, 168

construction, 7, 14, 53, 208, 230 constructivism, 6

consumption, 37, 38, 57 contour, 192, 206 contradiction, 4, 5 convergence, 48, 81, 150, 272

copper, 123, 124, 125, 140, 141, 142, 143, 144, 145, 146

correlations, 1, 7, 9, 10, 16, 17 cost, 37, 39, 49, 268

creep, 168, 170, 186, 191, 194, 196, 199, 221, 224, 225

cryptography, 35

D

damping, vii, 69, 140, 167, 194, 199, 210, 216, 217, 220, 222, 224, 225, 286

data analysis, 274 data structure, 287 decay, 153, 228

decomposition, 15, 38, 40, 46, 56, 57, 58 deconstruction, 6, 7, 12

deformation, 177, 181, 183, 217, 221 degenerate, 11, 208

depth, 106, 243, 244, 246, 252

derivatives, viii, 25, 26, 44, 59, 62, 66, 123, 150, 151, 152, 158, 165, 166, 167, 169, 188, 191, 192, 201, 211, 220, 223, 224, 225, 233, 262, 263, 285

diesel engines, 58

differential equations, 1, 8, 19, 23, 34, 35, 61, 66, 151, 161, 221, 287, 288

diffusion, viii, ix, 4, 8, 11, 15, 24, 93, 94, 106, 108, 119, 124, 227, 228, 229, 230, 231, 232, 233, 235, 236, 237, 238, 239, 240, 241, 243, 246, 247, 256, 260

diffusion process, 15 diffusion time, 108 diffusivity, 95, 106, 124, 228 direct action, 287

discontinuity, 154, 158, 208, 210 discretization, 272, 273, 288 disequilibrium, 10

disordered systems, 247 dispersion, 200, 221, 240, 241

displacement, 42, 69, 210, 215, 232, 247 disposition, 256

distribution, vii, 2, 3, 5, 15, 16, 17, 18, 40, 53, 134, 194, 199, 216, 218, 249, 252

distribution function, 194, 199, 216 divergence, 11, 18

dosing, 243, 256

drug release, 244, 247, 256 drugs, 243, 248, 255, 256

DSC, 163 duality, 11, 129

dynamic systems, 60, 62, 267 dynamical properties, 23, 26, 269

dynamical systems, 23, 24, 88, 149, 162, 274

E

elastic deformation, 53 electrochemistry, 20, 93 electrodes, 16 electrolyte, 2 electromagnetic, 287 electromagnetism, 93 electrons, 3

energy, 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 15, 16, 17, 18, 19, 20, 42, 81, 88, 95, 227, 228, 240, 243

energy consumption, 20

engineering, viii, ix, 4, 12, 18, 69, 150, 154, 161, 162, 168, 215, 224, 243, 274

England, 62, 286

entropy, 3, 6, 7, 9, 11, 15, 17, 18

environment, 2, 7, 10, 11, 13, 17, 18, 49, 53, 243, 247, 274

environmental policy, 37, 38 equality, 213, 214, 215

equilibrium, 7, 9, 10, 14, 23, 24, 25, 27, 28, 37, 40, 43, 44, 45, 47, 55, 81, 84, 86, 194, 210, 216, 232, 240

equipment, 49 Euclidean space, 11

evolution, 81, 210, 268, 287 execution, 274

exponential functions, 6

F

families, 263, 267, 268, 270 FDA, viii, 59, 60, 285, 287 fidelity, 130

filters, 263

financial support, 88, 255 fish, 260, 274

fitness, 268, 275 flatness, 67

flexibility, 39, 50, 66, 161, 260, 269 fluid, 24, 42, 53, 158, 167

force, 4, 42, 81, 181, 182, 192, 215, 216, 217, 219, 230

Ford, 34

formula, vii, 41, 42, 51, 53, 67, 151, 166, 167, 171, 172, 173, 175, 176, 179, 189, 192, 204, 206, 213, 215, 217, 218, 219, 234, 252, 272

foundations, 1, 165, 260 fractal dimension, 4, 5, 6, 10 fractal space, 5, 6, 10, 11 fractal structure, 2, 16, 17

fractality, 1, 4, 5, 6, 10, 13, 18

fractional differentiation, 20, 66, 123, 148, 225 fractional order differential equations, 35, 151 fractional order systems, 24, 25, 30, 46, 66, 67, 89,

93, 121, 123, 124, 162, 288

France, vii, viii, 21, 34, 59, 60, 61, 89, 90, 93, 123, 147, 285

freedom, 15, 39, 48, 50

friction, 42, 53, 81, 167, 181, 182, 221, 222 fuel consumption, 37, 38

fuzzy set theory, 260

G

general anesthesia, ix, 248, 256 geometrical parameters, 42

geometry, 1, 2, 3, 4, 6, 7, 10, 11, 15, 20, 56, 217 glue, 125

gravity, 19, 81, 263 groundwater, 230

H

half-integer order controller, vii half-integer orders, vii

heart rate, 252 heat capacity, 95 height, 221, 249

heredity, 168, 172, 208, 210, 212, 217, 219 historical overview, 169

history, viii, 24, 257 homogeneity, 5 human body, 245 Hungary, 89 Hunter, 217, 221 hybrid, 286

hyperbolic systems, 18 hypnosis, 244

I

ideal, 16, 39, 58, 65, 67, 68, 77, 78, 87, 88, 167, 262, 285

identification, 47, 62, 93, 94, 119, 120, 147, 148, 252, 253, 254

identity, 11, 180 impulses, 247 impulsive, 221 independence, 3, 10 India, 23, 256 individuals, 268, 274

induction, 120, 124, 147, 250 industry, 6, 38, 39, 57, 58, 61, 90, 261 inequality, 17, 25, 158, 213

inertia, 42, 81, 167, 215, 275 inhibitor, 239

injections, 56

integration, 39, 46, 48, 49, 53, 66, 67, 68, 72, 73, 94, 98, 101, 111, 112, 115, 116, 120, 148, 150, 151, 192, 213, 261, 273

intelligence, 260, 274, 275 intensive care unit, 256

interface, ix, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 49, 93, 94, 96, 106, 119, 120, 124, 146

interrogations, 4 invariants, 4

inversion, 6, 16, 19, 192, 204, 206, 218, 220, 233 ions, 3

Iran, 149

Ireland, 58

iron, 123, 124, 125, 140, 141, 142, 143, 144, 145, 146

Italy, viii, 37, 60, 146 iteration, 132, 275

J

Japan, 60, 89

Jordan, 192, 193

K

kinetics, 241, 243, 247, 256 Korea, 62

L

laws, 2, 13, 167, 220, 228, 247

lead, 11, 18, 50, 54, 57, 136, 148, 227, 247, 276, 277, 278

leakage, 11

lean body mass, 249 Lebanon, 93, 120, 123, 146 light, 248

linear law, 221

linear model, 38, 40, 44, 46, 53, 83, 85, 131 linear systems, 88, 162

liquids, 20 lithium, 20

locus, 196, 206, 208, 218 LPG, 58

LTD, 222

Luo, 59, 60, 162

Lyapunov function, 155, 156

M

machine learning, 286 macromolecules, 168 magnet, 162

magnitude, 49, 50, 68, 102, 179, 189, 192, 194, 196, 202, 206, 208, 212, 213

management, 275

mapping, 10, 12, 263, 265, 267, 274, 284

mass, vii, 41, 42, 81, 84, 85, 86, 87, 192, 199, 215, 223, 227, 228, 230, 245, 249

mass-damping, vii

materials, 123, 124, 125, 126, 128, 146, 167, 168, 177, 200, 217, 225, 262

mathematics, 6, 20

matrix, 24, 25, 27, 31, 70, 76, 79, 257

matter, 2, 3, 4, 7, 44, 227, 228, 230, 231, 232, 239 measurement(s), 3, 5, 6, 9, 11, 15, 17, 83, 94, 106,

131, 132, 146

media, 3, 5, 6, 7, 20, 117, 119, 165, 166, 168, 208, 210, 212, 219, 228

median, 139

medicine, 243, 256, 257

membership, 263, 267, 268, 269, 270, 274, 275 memory, 24, 45, 167, 212, 220, 222, 227, 228, 231,

240, 262, 267, 275 metals, 241

methodology, 38, 40, 46, 47, 49, 57, 88, 93, 259, 260, 261, 270, 283, 285

microwaves, 2

Ministry of Education, 219 mixing, 15, 16, 17

mobile robots, 80

modelling, viii, 24, 257, 275, 288

models, vii, 9, 24, 39, 43, 44, 66, 91, 119, 131, 150, 167, 168, 169, 171, 188, 189, 191, 199, 200, 220, 224, 225, 243, 244, 245, 246, 247, 248, 249, 251, 252, 255, 256, 257

modulus, 171, 177, 178, 190, 192, 193, 194, 196, 215, 216, 217, 219

moisture, 120 momentum, 10, 41 monomers, 16 Montana, 147

Moscow, 222, 223, 224, 241 motion control, 59, 60 motivation, 39, 69 multiplication, 6, 16, 165, 173 multiplier, 233

mutation, 268, 269, 270

N

natural gas, 37, 38, 59 natural selection, 268 nerve, 247 Netherlands, 61, 287

neural network(s), 274, 287 neurotransmitters, 247 non-integer differentiation, vii, viii non-integer models, vii

nonlinear dynamics, 239, 243, 260 nonlinear systems, 153, 161, 162, 284, 286

nonlocality, 24 null, 219, 262

numerical applications, vii numerical computations, 235

O

one dimension, 3 operating range, 47, 53, 55 operations, 55 opportunities, 6, 19

optimization, 2, 6, 93, 119, 147, 162, 225, 255, 259, 260, 268, 269, 270, 274, 275, 286, 287, 288

orthogonality, 216

P

pain, 244, 245, 246, 247, 248 parallel, 223

parallelism, 268 parameter estimation, 150 partition, 6, 17

path integrals, 9 percolation, 2, 247 pharmacokinetics, 256, 257 pharmacology, 256

phase diagram, 49, 50, 183 physical characteristics, 97, 108 physical environment, 2 physical phenomena, 12

physics, viii, ix, 4, 5, 6, 18, 19, 93, 162, 247, 286 physiology, 257

plane waves, 225

plants, 39, 49, 150, 158, 161, 260, 261, 267 platinum, 125

Poincaré, 9, 10, 11, 12 Poisson ratio, 232 Poland, 227

polar, 234, 237 polarization, 124 polycarbonate, 200 polymer, 200, 221, 247 polymer systems, 221 polymeric materials, 168

polymers, 16, 168, 200, 221, 225, 247 polymorphism, 53

population, 252, 269, 270, 276 population size, 269, 270 porosity, 247

porous media, 24, 230 Portugal, viii, 59, 259 POWER, 1

process control, 93, 94, 119 project, viii, 33, 58, 88

propagation, 43, 44, 165, 168, 220, 221, 223 prototypes, 38, 40

pumps, 158, 159

Q

quantum mechanics, 19

R

radius, 215

random walk, 239, 240, 247 reactions, 246, 251, 252 reasoning, 259, 284, 285 recall, viii, 4, 7, 13, 69, 252 recovery, 243

regulations, 37, 38 rejection, 38

relaxation, 7, 168, 171, 181, 183, 186, 188, 190, 191, 194, 196, 197, 198, 199, 200, 201, 203, 207, 208, 209, 215, 218, 219, 221, 222, 224, 225, 240

relaxation process, 168, 208, 225 relaxation processes, 168, 208, 225 relaxation times, 183, 191, 208 relevance, 2, 10

renormalization, 16, 18 reserves, 2

residues, 193 resistance, 10, 125 resonator, 90 resources, 286 respiratory rate, 252

response, 1, 9, 18, 30, 31, 38, 43, 48, 49, 50, 54, 56, 60, 67, 69, 78, 87, 94, 98, 101, 102, 103, 111, 112, 114, 115, 126, 128, 130, 134, 139, 140, 141, 142, 143, 144, 159, 168, 215, 217, 224, 240, 249, 250, 256, 260, 271, 272, 273, 275, 276, 277, 278, 281

responsiveness, 257 restrictions, 51

retardation, 168, 171, 181, 186, 188, 191, 194, 196, 200, 203, 204, 205, 218, 224

robotics, 260

roots, 11, 25, 46, 47, 69, 75, 96, 174, 176, 180, 189, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 206, 207, 208, 209, 216

rotations, 14

rules, ix, 1, 16, 18, 45, 48, 50, 54, 61, 259, 260, 265, 267, 268, 274

Russia, 1, 165, 224

S

safety, 37, 38

saturation, 55, 56, 81, 89, 135, 260, 265, 273, 284 scaling, 1, 3, 4, 5, 7, 11, 17, 20, 245, 247, 252, 265,

267

scaling law, 1, 247 search space, 268

second generation, 123, 125, 132, 146 secure communication, 29

self-organization, 19 semicircle, 6, 7

sensitivity, 37, 45, 131, 135, 136, 137, 138, 250 sensors, 58, 69, 244

shape, 57, 68

shear, 178, 181, 183 shear deformation, 181

shock, 165, 208, 210, 211, 212, 215, 219, 220, 223 shock waves, 165, 208, 210, 219

showing, ix, 167, 260, 284

signals, 31, 32, 33, 35, 42, 44, 128, 247, 252 signs, 176, 210

simulation, 38, 40, 45, 53, 54, 55, 57, 60, 66, 94, 101, 118, 120, 128, 130, 139, 141, 147, 149, 150, 151, 159, 162, 252, 259, 267, 274, 276, 280

Singapore, 58, 162, 257, 286 social learning, 275

society, 19, 285, 286 software, 40

solid state, 167

solution, 7, 23, 34, 45, 67, 75, 83, 96, 107, 168, 176, 192, 193, 194, 196, 197, 201, 202, 203, 204, 205, 210, 211, 216, 218, 220, 235, 236, 237, 239, 247, 254, 275

space-time, 4, 5, 10, 19, 241 Spain, viii, 90, 285

species, 2, 3, 274

specifications, 38, 40, 45, 48, 49, 51, 57, 131, 132, 135, 141, 145, 261, 281

speech, 19 spinal cord, 247

St. Petersburg, 224

stability, vii, 23, 24, 27, 38, 40, 45, 46, 47, 48, 49, 50, 55, 56, 57, 58, 59, 66, 67, 69, 75, 76, 81, 84, 87, 123, 124, 132, 133, 135, 137, 138, 140, 145, 146, 149, 155, 156, 285

stability-precision, vii

stabilization, 59, 65, 66, 69, 80, 83, 84, 85, 87, 89, 90, 159

stabilizers, 288 stable states, 16

state, ix, 7, 10, 14, 15, 23, 40, 42, 43, 49, 56, 65, 66, 67, 69, 70, 72, 73, 75, 76, 77, 79, 80, 82, 83, 84, 85, 86, 87, 88, 89, 90, 119, 121, 132, 135, 137, 138, 140, 145, 149, 152, 158, 159, 162, 165, 166, 167, 232, 244, 245, 248, 266, 270, 271, 276

states, 10, 14, 16, 95, 106, 152 statistics, 5, 20

steel, 40, 217 stimulus, 247 storage, 2, 6, 12 strategy use, 81

stress, 168, 171, 181, 190, 210, 220, 232, 236, 237, 238, 245

structure, 2, 3, 4, 11, 12, 16, 17, 18, 20, 27, 94, 168, 216, 223, 228, 230, 256, 274, 278

style, 267 Sun, 59, 62

superconductivity, 19

suppression, 69, 150 swarm intelligence, 274 Switzerland, 60 symmetry, 4, 6, 23

synchronization, 23, 29, 30, 31, 32, 33, 34, 35 synchronize, 30

synthesis, vii, ix, 38, 52, 57, 60, 62, 94, 130 system analysis, 62, 284

T

Taiwan, 285

tanks, ix, 158, 159, 161, 163 target, 217, 221, 250, 252, 257

techniques, 30, 48, 52, 154, 255, 260, 268, 274, 285 technologies, 58

technology, 66, 146, 284

temperature, 41, 53, 94, 96, 97, 99, 101, 103, 104, 106, 107, 108, 109, 110, 111, 114, 116, 117, 118, 123, 124, 125, 139, 140, 141, 142, 143, 144, 145, 146, 227, 228, 229, 230

testing, 55, 59, 121, 148 thermodynamic equilibrium, 7 thermodynamics, 9, 167

time increment, 262 time series, 28, 29 torus, 9, 13

tracks, 146

trajectory, 152, 159, 222 transduction, 247

transformation, 7, 26, 38, 41, 70, 73, 76, 77, 79, 192, 204, 212

transmission, 80, 247

transport, 2, 3, 4, 5, 9, 15, 230, 239, 240, 241, 246 transport processes, 230, 239

transportation, 3, 10, 18

Turkey, viii, 287

U

U.S. Army Corps of Engineers, 121

United States (USA), 10, 35, 62, 88, 171, 223, 284 USSR, 150

universality, 21 universe, 265, 267 USSR, 150

V

validation, 53, 94

valve, 37, 38, 40, 42, 44, 54, 55, 56

variables, 3, 42, 45, 46, 53, 54, 69, 82, 152, 212, 221, 234, 239, 265

variations, 37, 38, 39, 41, 44, 45, 46, 48, 49, 50, 53, 55, 56, 57, 58, 68, 123, 125, 132, 146, 159, 211 vector, 65, 70, 76, 79, 82, 152, 210, 228, 229, 230,

232 vehicles, 37, 38

velocity, 4, 69, 83, 162, 210, 215, 217, 227, 230, 275 vibration, 69, 89, 90, 150, 167, 197, 199

viscoelastic properties, 199 viscosity, 19, 181, 210, 220

W

water, ix, 158, 159, 161 wave propagation, 168 wear, 150, 154

working conditions, 39, 40, 43, 45, 46, 56