| Preface |
| Acknowledgments |
| Special Functions of Preface |
| Acknowledgements |
| Special Functions of the Fractional Calculuslt |
| Gamma Function |
| Mittag-Leffler Function |
| Wright Function |
| Fractional Derivatives and Integralslt |
| The Name of the Game |
| Gruuml;nwald-Letnikov Fractional Derivatives |
| Riemann-Liouville Fractional Derivatives |
| Some Other Approaches |
| Sequential Fractional Derivatives |
| Left and Right Fractional Derivatives |
| Properties of Fractional Derivatives |
| Laplace Transforms of Fractional Derivatives |
| Fourier Transforms of Fractional Derivatives |
| Mellin Transforms of Fractional Derivatives |
| Existence and Uniqueness Theoremslt |
| Linear Fractional Differential Equations |
| Fractional Differential Equation of a General Form |
| Existence and Uniqueness Theorem as a Method of Solution |
| Dependence of a Solution on Initial Conditions |
| The Laplace Transform Methodlt |
| Standard Fractional Differential Equations |
| Sequential Fractional Differential Equations |
| Fractional Green's Functionlt |
| Definition and Some Properties |
| Term Equation / One： |
| Term Equation. / Two： |
| Calculation of Heat Load Intensity Change in Blast Furnace Walls / Four： |
| Finite-Part Integrals and Fractional Derivatives |
| General Case: nlt;/i>-term Equation |
| Other Methods for the Solution of Fractional-order Equationslt |
| The Mellin Transform Method |
| Power Series Method |
| Babenko's Symbolic Calculus Method |
| Method of Orthogonal Polynomials |
| Numerical Evaluation of Fractional Derivativeslt |
| Approximation of Fractional Derivatives |
| The "Short-Memory" Principle |
| Order of Approximation |
| Computation of Coefficients |
| Higher-order Approximations |
| Numerical Solution of Fractional Differential Equationslt |
| Initial Conditions: Which Problem to Solve? Numerical Solution |
| Examples of Numerical Solutions |
| The "Short-Memory" Principle in Initial Value Problems for Fractional Differential Equations |
| Fractional-Order Systems and Controllers |
| Fractional-Order Systems and Fractional-Order Controllerslt |
| Example |
| on Viscoelasticity |
| Bode's Analysis of Feedback Amplifiers |
| Fractional Capacitor Theory |
| Electrical Circuits |
| Electroanalytical Chemistry |
| Electrode-Electrolyte Interface |
| Fractional Multipoles |
| Biology |
| Fractional Diffusion Equations |
| Control Theory |
| Fitting of Experimental Data |
| The "Fractional-Order" Physics? Bibliography |
| Tables of Fractional Derivativeslt |
| Index |
| Preface |
| Acknowledgments |
| Special Functions of Preface |
図書
