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Table of Contents
Intro; Preface; Contents; 1 Elements of Time Scale Calculus; 1.1 Forward and Backward Jump Operators, Graininess Function; 1.2 Differentiation; 1.3 Mean Value Theorems; 1.4 Integration; 1.5 The Exponential Function; 1.5.1 Hilger's Complex Plane; 1.5.2 Definition and Properties of the Exponential Function; 1.5.3 Examples for Exponential Functions; 1.6 Hyperbolic and Trigonometric Functions; 1.7 Dynamic Equations; 1.8 Power Series on Time Scales; 1.9 Advanced Practical Problems; 2 The Laplace Transform on Time Scales; 2.1 Definition and Properties
9.2 Inhomogeneous Caputo Fractional Dynamic Equations with Constant Coefficients9.3 Advanced Practical Problems; 10 Appendix: The Gamma Function; 10.1 Definition of the Gamma Function; 10.2 Some Properties of the Gamma Function; 10.3 Limit Representation of the Gamma Function; 11 Appendix: The Beta Function; 11.1 Definition of the Beta Function; 11.2 Properties of the Beta Function; 11.3 An Application; References; Index
9.2 Inhomogeneous Caputo Fractional Dynamic Equations with Constant Coefficients9.3 Advanced Practical Problems; 10 Appendix: The Gamma Function; 10.1 Definition of the Gamma Function; 10.2 Some Properties of the Gamma Function; 10.3 Limit Representation of the Gamma Function; 11 Appendix: The Beta Function; 11.1 Definition of the Beta Function; 11.2 Properties of the Beta Function; 11.3 An Application; References; Index