Page 704 - Mathematical Techniques of Fractional Order Systems

676 Index

Thermal combustion theory, 38 fuzzy adaptive robust H ( control, 603 607
Three-point boundary value problem, 63 69 simulation results, 610 616
Time-delay-dependent stability condition, stability analysis, 607 609
feedback stabilization based on, T S fuzzy systems, basics and description
149 150 of, 602 603
Time-delay-independent stability condition, Unidirectional coupling mode, 626 627
feedback stabilization based on, Unity-feedback control system, 97
148 149 Upper semicontinuous (u.s.c), 189 190,
Time-domain methods, 138 233 234
Time-varying delays, stability analysis in
presence of, 138 147
time-delay-dependent stability, 143 147 V
time-delay-independent stability, 139 143 Variable order fractional derivatives, 1 2,
Topological synchronization, 641 644 4 9
of fractional order Lorenz’s systems, application example, 3
644 651 creating compact biochemical bone
of fractional order Ro ¨ssler’s systems, remodeling models, 23 31
651 656 definitions, 5 9
Topology of fractional order space, 636 639 Gru ¨nwald Letnikoff (GL) definition, 5 6
Tracking error vector, 604 intuitive results for integer
Traditional synchronization, 639 641 orders, 4 5
Trajectory tracking task, tuning of controller Riemann Liouville (RL) definition, 5 6
for, 266 269 variables and parameters, 32t
Transforming Growth Factor-β (TGF-β), Variational iteration method (VIM), 37,
12 13 44 45, 51 53, 58 60
Transient response, 80, 391t Vertical scaling and zooming maps, 382 383,
Trapping time, 631, 632t 396 399, 402
Trend, 632, 632t Vitamin D, 12
T S fuzzy systems Volta’s system
basics and description of, 602 603 fractional-order, 354
Tumor-derived proteases, 13 phase portraits of, 356f
Two-channel secure communication, 423 427 Volterra integral equations, 103 105, 109
Two-link planar rigid robotic manipulator V-shape input output profile, 262 263
system, 252 253, 253f, 256t
Type-1 variable order derivatives, 6 W
Type-2 variable order derivatives, 7
Type-3 variable order derivatives, 7 8 w-domain expressions, 78
Type-A variable order, 8 9 Wnt-signaling, 12 13
Type-B variable order derivatives, 6 Wolf algorithm, 327
Type-C variable order derivatives, 7 Wolfram Mathematica, 47
Type-D variable order derivatives, 7 8 Wu fractional logistic map, dynamics of,
388 392
U Z
Ultraslow diffusion equations, 103 105
“0 1” test, 491
Uncertain fractional order chaotic systems
Zero-order deformation equation, 40 43
synchronization, 597
Zoledronic acid, 13 14
basic definition and preliminaries for
Zooming map, 382 383, 396 399
fractional calculus, 599 602