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The Fractional Trigonometry : With Applications to Fractional Differential Equations and Science.
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Somerset :
Wiley,
2016.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Title Page; Copyright; Table of Contents; Preface; Acknowledgments; About the Companion Website; Chapter 1: Introduction; 1.1 Background; 1.2 The Fractional Integral and Derivative; 1.3 The Traditional Trigonometry; 1.4 Previous Efforts; 1.5 Expectations of a Generalized Trigonometry and Hyperboletry; Chapter 2: The Fractional Exponential Function via the Fundamental Fractional Differential Equation; 2.1 The Fundamental Fractional Differential Equation; 2.2 The Generalized Impulse Response Function; 2.3 Relationship of the F-function to the Mittag-Leffler Function.
- 2.4 Properties of the F-Function2.5 Behavior of the F-Function as the Parameter a Varies; 2.6 Example; Chapter 3: The Generalized Fractional Exponential Function: The R-Function and Other Functions for the Fractional Calculus; 3.1 Introduction; 3.2 Functions for the Fractional Calculus; 3.3 The R-Function: A Generalized Function; 3.4 Properties of the Rq, v(a, t)-Function; 3.5 Relationship of the R-Function to the Elementary Functions; 3.6 R-Function Identities; 3.7 Relationship of the R-Function to the Fractional Calculus Functions; 3.8 Example: Cooling Manifold.
- 3.9 Further Generalized Functions: The G-Function and the H-Function3.10 Preliminaries to the Fractional Trigonometry Development; 3.11 Eigen Character of the R-Function; 3.12 Fractional Differintegral of the Timescaled R-Function; 3.13 R-Function Relationships; 3.14 Roots of Complex Numbers; 3.15 Indexed Forms of the R-Function; 3.16 Term-by-Term Operations; 3.17 Discussion; Chapter 4: R-Function Relationships; 4.1 R-Function Basics; 4.2 Relationships for Rm,0 in Terms of R1,0; 4.3 Relationships for R1/m,0 in Terms of R1,0; 4.4 Relationships for the Rational Form Rm/p,0 in Terms of R1/p,0.
- 4.5 Relationships for R1/p,0 in Terms of Rm/p,04.6 Relating Rm/p,0 to the Exponential Function R1,0(b, t) = ebt; 4.7 Inverse Relationships
- Relationships for R1,0 in Terms of Rm, k; 4.8 Inverse Relationships
- Relationships for R1,0 in Terms of R1/m,0; 4.9 Inverse Relationships
- Relationships for eat = R1,0(a, t) in Terms of Rm/p,0; 4.10 Discussion; Chapter 5: The Fractional Hyperboletry; 5.1 The Fractional R1-Hyperbolic Functions; 5.2 R1-Hyperbolic Function Relationship; 5.3 Fractional Calculus Operations on the R1-Hyperbolic Functions; 5.4 Laplace Transforms of the R1-Hyperbolic Functions.
- 5.5 Complexity-Based Hyperbolic Functions5.6 Fractional Hyperbolic Differential Equations; 5.7 Example; 5.8 Discussions; Chapter 6: The R1-Fractional Trigonometry; 6.1 R1-Trigonometric Functions; 6.2 R1-Trigonometric Function Interrelationship; 6.3 Relationships to R1-Hyperbolic Functions; 6.4 Fractional Calculus Operations on the R1-Trigonometric Functions; 6.5 Laplace Transforms of the R1-Trigonometric Functions; 6.6 Complexity-Based R1-Trigonometric Functions; 6.7 Fractional Differential Equations; Chapter 7: The R2-Fractional Trigonometry.