Intro
Preface
Contents
1 Mathematical Background of Deterministic Fractals
1.1 Introduction
1.2 Iterated Function System
1.3 Countable Iterated Function System
1.4 Local Countable Iterated Function System
1.4.1 Local Iterated Function System
1.4.2 Existence and Analytical Properties of LCIFS
1.5 Fractal Dimension
1.6 Generalized Fractal Dimensions
1.6.1 Some Special Cases
1.6.2 Limiting Cases of Generalized Fractal Dimensions
1.6.3 Range of Generalized Fractal Dimensions
1.7 Concluding Remarks
2 Fractal Functions
2.1 Introduction

2.2 Interpolation Functions
2.3 Fractal Interpolation Function
2.4 Hidden Variable Fractal Interpolation Function
2.5 Classical Calculus on Fractal Interpolation Functions
2.6 Concluding Remarks
3 Fractional Calculus on Fractal Functions
3.1 Introduction
3.2 Linear Fractal Interpolation Function
3.3 Riemann-Liouville Fractional Calculus Quadratic FIF
3.4 Fractal Dimension
3.5 Fractional Calculus of Quadratic FIF with Variable Scaling Factors
3.6 Concluding Remarks
4 Fractal Interpolation Function for Countable Data
4.1 Introduction

4.2 Existence of FIF for Countable Data Set
4.3 Fractional Calculus on Interpolation Function of Sequence of Data
4.4 Concluding Remarks
5 Multifractal Analysis and Wavelet Decomposition in EEG Signal Classification
5.1 Introduction
5.2 Experimental Signals
5.2.1 Synthetic Weierstrass Signals
5.2.2 Clinical EEG Signals
5.3 Statistical Methods
5.3.1 ANOVA Test
5.3.2 Box Plot
5.3.3 Normal Probability Plot
5.4 Development of Multifractal Analysis in EEG Signal Classification
5.4.1 Modified Generalized Fractal Dimensions

5.4.2 Improved Generalized Fractal Dimensions
5.4.3 Advanced Generalized Fractal Dimensions
5.4.4 Methods to Analyze the Fractal Time Signals
5.4.5 Results and Discussions
5.5 Multifractal-Wavelet Based Denoising in EEG Signal Classification
5.5.1 Discrete Wavelet Transform
5.5.2 Wavelet Denoising of Signals
5.5.3 Results and Discussions
5.6 Concluding Remarks
6 Fuzzy Multifractal Analysis in ECG Signal Classification
6.1 Introduction
6.2 Fuzzy Multifractal Analysis for Fractal Signals
6.2.1 Fuzzy Renyi Entropy

6.2.2 Fuzzy Generalized Fractal Dimensions for Signals
6.3 Fuzzy Generalized Fractal Dimensions for Deterministic Fractal Waveforms
6.4 Experimental ECG Data
6.5 Fuzzy Generalized Fractal Dimensions for Clinical ECG Signals
6.6 Concluding Remarks
Appendix References