Fractional Trigonometry
-15%
portes grátis
Fractional Trigonometry
With Applications to Fractional Differential Equations and Science
Lorenzo, Carl F.; Hartley, Tom T.
John Wiley & Sons Inc
12/2016
464
Dura
Inglês
9781119139409
15 a 20 dias
952
Descrição não disponível.
Preface xv
Acknowledgments xix
About the Companion Website xxi
1 Introduction 1
2 The Fractional Exponential Function via the Fundamental Fractional Differential Equation 9
3 The Generalized Fractional Exponential Function: The R-Function and Other Functions for the Fractional Calculus 19
4 R-Function Relationships 47
5 The Fractional Hyperboletry 63
6 The R1-Fractional Trigonometry 79
7 The R2-Fractional Trigonometry 97
8 The R3-Trigonometric Functions 129
9 The Fractional Meta-Trigonometry 159
10 The Ratio and Reciprocal Functions 217
11 Further Generalized Fractional Trigonometries 229
Introduction to Applications 241
12 The Solution of Linear Fractional Differential Equations Based on the Fractional Trigonometry 243
13 Fractional Trigonometric Systems 259
14 Numerical Issues and Approximations in the Fractional Trigonometry 271
15 The Fractional Spiral Functions: Further Characterization of the Fractional Trigonometry 283
16 Fractional Oscillators 309
17 Shell Morphology and Growth 317
18 Mathematical Classification of the Spiral and Ring Galaxy Morphologies 341
19 Hurricanes, Tornados, and Whirlpools 371
20 A Look Forward 381
A RelatedWorks 389
B Computer Code 393
C Tornado Simulation 399
D Special Topics in Fractional Differintegration 401
E Alternate Forms 413
References 417
Index 425
Acknowledgments xix
About the Companion Website xxi
1 Introduction 1
2 The Fractional Exponential Function via the Fundamental Fractional Differential Equation 9
3 The Generalized Fractional Exponential Function: The R-Function and Other Functions for the Fractional Calculus 19
4 R-Function Relationships 47
5 The Fractional Hyperboletry 63
6 The R1-Fractional Trigonometry 79
7 The R2-Fractional Trigonometry 97
8 The R3-Trigonometric Functions 129
9 The Fractional Meta-Trigonometry 159
10 The Ratio and Reciprocal Functions 217
11 Further Generalized Fractional Trigonometries 229
Introduction to Applications 241
12 The Solution of Linear Fractional Differential Equations Based on the Fractional Trigonometry 243
13 Fractional Trigonometric Systems 259
14 Numerical Issues and Approximations in the Fractional Trigonometry 271
15 The Fractional Spiral Functions: Further Characterization of the Fractional Trigonometry 283
16 Fractional Oscillators 309
17 Shell Morphology and Growth 317
18 Mathematical Classification of the Spiral and Ring Galaxy Morphologies 341
19 Hurricanes, Tornados, and Whirlpools 371
20 A Look Forward 381
A RelatedWorks 389
B Computer Code 393
C Tornado Simulation 399
D Special Topics in Fractional Differintegration 401
E Alternate Forms 413
References 417
Index 425
Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.
fractional calculus;?linear commensurate-order fractional differential equations; fractional trigonometry; fractional exponential function; fundamental fractional differential equation; generalized exponential function; R-function relationships
Preface xv
Acknowledgments xix
About the Companion Website xxi
1 Introduction 1
2 The Fractional Exponential Function via the Fundamental Fractional Differential Equation 9
3 The Generalized Fractional Exponential Function: The R-Function and Other Functions for the Fractional Calculus 19
4 R-Function Relationships 47
5 The Fractional Hyperboletry 63
6 The R1-Fractional Trigonometry 79
7 The R2-Fractional Trigonometry 97
8 The R3-Trigonometric Functions 129
9 The Fractional Meta-Trigonometry 159
10 The Ratio and Reciprocal Functions 217
11 Further Generalized Fractional Trigonometries 229
Introduction to Applications 241
12 The Solution of Linear Fractional Differential Equations Based on the Fractional Trigonometry 243
13 Fractional Trigonometric Systems 259
14 Numerical Issues and Approximations in the Fractional Trigonometry 271
15 The Fractional Spiral Functions: Further Characterization of the Fractional Trigonometry 283
16 Fractional Oscillators 309
17 Shell Morphology and Growth 317
18 Mathematical Classification of the Spiral and Ring Galaxy Morphologies 341
19 Hurricanes, Tornados, and Whirlpools 371
20 A Look Forward 381
A RelatedWorks 389
B Computer Code 393
C Tornado Simulation 399
D Special Topics in Fractional Differintegration 401
E Alternate Forms 413
References 417
Index 425
Acknowledgments xix
About the Companion Website xxi
1 Introduction 1
2 The Fractional Exponential Function via the Fundamental Fractional Differential Equation 9
3 The Generalized Fractional Exponential Function: The R-Function and Other Functions for the Fractional Calculus 19
4 R-Function Relationships 47
5 The Fractional Hyperboletry 63
6 The R1-Fractional Trigonometry 79
7 The R2-Fractional Trigonometry 97
8 The R3-Trigonometric Functions 129
9 The Fractional Meta-Trigonometry 159
10 The Ratio and Reciprocal Functions 217
11 Further Generalized Fractional Trigonometries 229
Introduction to Applications 241
12 The Solution of Linear Fractional Differential Equations Based on the Fractional Trigonometry 243
13 Fractional Trigonometric Systems 259
14 Numerical Issues and Approximations in the Fractional Trigonometry 271
15 The Fractional Spiral Functions: Further Characterization of the Fractional Trigonometry 283
16 Fractional Oscillators 309
17 Shell Morphology and Growth 317
18 Mathematical Classification of the Spiral and Ring Galaxy Morphologies 341
19 Hurricanes, Tornados, and Whirlpools 371
20 A Look Forward 381
A RelatedWorks 389
B Computer Code 393
C Tornado Simulation 399
D Special Topics in Fractional Differintegration 401
E Alternate Forms 413
References 417
Index 425
Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.
