Page 691 - Mathematical Techniques of Fractional Order Systems

Index

Note: Page numbers followed by “f” and “t” refer to figures and tables, respectively.

A Asymptotic response, 76, 80
Atangana Baleanu’s fractional derivative,
Abstract phase space, 209
226
Active backstepping technique, 576 581,
Attractor
585f, 587f
chaotic, 475 476, 479f
controller design for stabilization, 576 579
defined, 504
synchronization using, 579 581
hidden, 504 505, 507 516, 508t
Active control functions, 332, 336
self-excited, 411
Active control technique, 322, 325, 330 331,
Automatic voltage regulator (AVR), 160
340, 626 627
Adams Bashforth Moulton algorithm, 414,
490 491, 505 506, 600 601 B
Adaptive control, 159 161, 453, 486, Backstepping technique, 562, 569 576,
626 627 582 585, 582f, 584f
Adaptive laws (AL), 159, 165 166, 598 controller design
Adaptive neuro-fuzzy inference system for stabilization, 570 574
(ANFIS), 250 for synchronization, 574 576
Adaptive observers and estimation, 160 Balder’s theorem, 208, 225
Adaptive terminal sliding mode Banach contraction mapping principle, 187,
synchronization for chaotic and 202
hyperchaotic systems, 292 294 Banach space, 186 187, 202, 207, 209, 211,
Adomian decomposition method (ADM), 37, 215, 222 223, 234 235
41 43, 51 53, 70 Barbalat’s lemma, 487
(a, k)-regularized resolvent family, 186 187, Barbalat’s Lyapunov-like stability theorem,
190 191, 202, 225 226 284
Alendronate, 13 14, 17 19 Basic Multicellular Unit (BMU), 9 11,
Anomalous diffusion, 1 2 29 32
Antisynchronization, 420, 426 427, 476, Bezout identity, 159 160
626 627, 640 Bifurcation diagrams, 376 377, 380,
state errors of the, 486 382 384
of two identical systems without of conventional map, 389f
equilibrium, 483 488 of fractional order map, 389f
Approximate controllability, 187, 193 201 of generalized logistic map, 386f
of multivalued fractional stochastic integro- of transition map, 388f
differential equation, 187 201 Bilinear matrix inequality (BMI) structure,
Arenodo system, 437 438, 455 150
Arteriovenous stenosis, evaluation of Bisphosphonates, 13 14, 17 19
in hemodialysis patients, 429 431 BMP (bone morphogenetic protein) receptors,
Artificial neural networks (ANN), 250 251 12
Arzela Ascoli theorem, 201 202, 216 219, Bohnenblust Karlin fixed point theorem, 187,
242 230 231, 246 247

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