Page 701 - Mathematical Techniques of Fractional Order Systems

Index 673

Nonidentical synchronization of complex Osteoblasts, 3, 9 12
chaotic systems, 298 299 evolution, 19f,20f
Noninteger order derivatives, 135 nonlocal simulation of, 22f,25f,31f
Nonlinear classical controllers, 249 250 Osteoclastogenesis, 12
Nonlinear complex systems, fractional order Osteoclasts, 3, 9 12
fuzzy sliding mode controller design evolution, 19f,20f
for. See Fractional order fuzzy sliding nonlocal simulation of, 22f,25f,31f
mode controller design for nonlinear Osteolytic metastases, 13
complex systems Oustaloup numerical approximation, 174
Nonlinear fractional order boundary-value
problems with multiple solutions, 37
applications, 45 69 P
Bratu’s problem, 58 63 Pade ´ technique, 93 94
heat transfer model and diffusion- Parameter estimation error dynamics, 486
reaction model, 51 57 Parathyroid hormone-related protein (PTHrP),
mixed convection flows in a vertical 13
channel, 45 51 Periodic remodeling cycles, 16 17
three-point boundary value problem, Permanent magnet synchronous motor
63 69 (PMSM), 436, 529
methods procedures, 39 45 chaos maps, 534 535
controlled Picard’s method (CPM), functions, 536t
43 45 chaotic behavior in, 533f
prediction of solutions multiplicity, 45 Chaotic Grasshopper Optimization
predictor homotopy analysis method, Algorithm, 539 542
39 43 Chaotic Grasshopper Optimizer strategy
Nonlinear variable order control scheme, (CGOA), 540 542
249 250 Grasshopper Optimization algorithm
Nonstandard finite difference (NSFD) scheme, (GOA) overview, 539 540
505 506 Chaotic Grey Wolf Optimization
Numerical simulation, 294 301, 625 626 Algorithm, 535 539
identical synchronization of fractional order Chaotic Grey Wolf Optimizer strategy
complex hyperchaotic systems, (CGWO), 539
299 301 Grey Wolf Optimization Algorithm
nonidentical synchronization of complex overview (GWO), 535 538
chaotic systems, 298 299 commensurate fractional order permanent
stabilization magnet synchronous motor model,
of fractional order complex Chen chaotic 543 547
system, 294 295 fractional order PMSM, 531 532
of fractional order complex Lorenz incommensurate fractional order permanent
hyperchaotic system, 296 297 magnet synchronous motor model,
Numerical Type-D formulation behavior, 27 548 555
Nussbaum gain, 165, 170 problem formulation, 532 534
Pharmacokinetics and pharmacodynamics
(PK/PD), 14 15
O Phase synchronization, 420
OGY method, 319 321 Picard’s method, 38, 43, 45
One-dimensional fractional order Bratu Poincare ´ recurrence diagrams,
equation, 58 60 643 644
Open Plus Close loop (OPCL), 452 Polynomial Diophantine equation, 79
OPG (Osteoprotegerin), 12 Positive map, 380
Optimal parameter estimations, 607 Power law for fractional order derivative, 568
Osteoblastic metastases, 13 Power series expansion (PSE), 429 430