Contents......Page 3
Preface......Page 9
Special Functions......Page 16
nitions and Properties of Fractional-Order Operators......Page 21
Laplace Transforms of Fractional-Order Operators......Page 25
Fractional-Order Systems [9]......Page 27
Controller [9]......Page 29
Triangular Orthogonal Functions......Page 30
Triangular Strip Operational Matrices for Classical and Fractional Derivatives......Page 46
References......Page 49
Processes represented by Weakly Singular Fredholm, Volterra & Volterra-Fredholm Integral Equations......Page 50
Existence and Uniqueness of Solution......Page 53
The Proposed Numerical Method......Page 56
Convergence Analysis......Page 60
Numerical Experiments......Page 63
Codes for Numerical Experiments......Page 76
Summary of Deliverables......Page 84
References......Page 85
Processes modeled by Abel Integral Equations......Page 87
Existence and Uniqueness of Solution......Page 90
The Proposed Numerical Method......Page 91
Convergence Analysis......Page 94
Numerical Experiments......Page 99
Codes for Numerical Experiments......Page 110
References......Page 118
Processes described by Fractional-Order Integro-Differential Equations......Page 122
Existence and Uniqueness of Solution......Page 123
The Proposed Numerical Method......Page 125
Convergence Analysis......Page 128
Numerical Experiments......Page 135
Codes for Numerical Experiments......Page 141
References......Page 145
Processes represented by Stiff & Nonstiff Fractional-Order DEs & Differential-Algebraic Equations......Page 147
Existence and Uniqueness of Solution......Page 148
The Proposed Numerical Method......Page 150
Convergence Analysis......Page 151
Numerical Experiments......Page 152
Codes for Numerical Experiments......Page 185
Concluding Remarks......Page 199
References......Page 200
Fractional Diffusion-Wave Equation......Page 203
The Proposed Numerical Method......Page 204
Convergence Analysis......Page 208
References......Page 210
Identification of Fractional Order Linear & Nonlinear Systems from Experimental or Simulated Data......Page 211
cation using TFs......Page 213
Simulation Examples......Page 218
MATLAB Codes for Simulation Examples......Page 230
Summary of Chapter Deliverables......Page 244
References......Page 245
Design of Fractional Order Controllers using Triangular Strip Operational Matrices......Page 247
Based Fractional Order Controller Design Method......Page 249
Constrained Nonlinear Optimization......Page 254
Simulation Examples......Page 258
MATLAB Codes for Simulation Examples......Page 277
Summary of Chapter Deliverables......Page 291
References......Page 292
Rational Integer Order System Approximation for Irrational Fractional Order Systems......Page 294
The Proposed Integer-Order Approximation Method......Page 297
Simulation Example......Page 301
MATLAB Codes for Simulation Example......Page 316
References......Page 319
Numerical Method for Solving Fractional Order Optimal Control Problems......Page 321
Proposed Numerical Method......Page 322
Simulation Examples......Page 325
Codes for Simulation Examples......Page 331
References......Page 337
Index......Page 339