## Table of Contents

**Table of Contents**

Foreword

Preface

About the Editors

Chapter 1 – Analysis of the Caputo Derivative and Pseudo State Representation with the Infinite State Approach (pp. 1-26)

Jean-Claude Trigeassou, Nezha Maamri and Alain Oustaloup (Département de Physique de l’Université Fédérale de Kazan Kremlevskaia, Russia)

Chapter 2 – Stability of a Class of Fractional Cauchy Problem (pp. 27-42)

Rabha W. Ibrahim (Department of Mathematics, Shivaji University, Kolhapur, India)

Chapter 3 – Numerical Solution of Fractional Order Differential Equations via Matrix-Based Methods (pp. 43-64)

Matthew Harker and Paul O’Leary (Dipartimento di Ingegneria Elettricaedell Informazione–Politecnico di Bari, Italy)

Chapter 4 – On Analytical Methods for Differential Equations with Local Fractional Derivative Operators (pp. 65-88)

Xiao-Jun Yang, Dumitru Baleanu and J. A. Tenreiro Machado (University Mouloud Mammeri of Tizi-Ouzou, Algeria and others)

Chapter 5 – Extended Borel Transform and Fractional Calculus (pp. 1-26)

Akira Asada (University of Bordeaux, IMS Laboratory, UMR 5218 CNRS, 33405 Talence, Bordeaux, France and others)

Chapter 6 – Introduction to Stability Theory of Linear Fractional Difference Equations (pp. 117-162)

Jan Čermák and Tomáš Kisela (University of Bordeaux, Laboratory IMS, UMR 5218 CNRS, 33405 Talence, Bordeaux, France and others)

Chapter 7 – Using the Hankel Operator to Initialize Fractional-Order Systems (pp. 163-182)

Jay L. Adams, Robert J. Veillette and Tom T. Hartley (Faculty of Electrical Engineering, Sharif University of Technology, Tehran, and Faculty of Electrical Engineering, Hamedan University of Technology, Hamedan, Iran)

Chapter 8 – Fractional Reaction-transport Equations Arising from Evanescent Continuous Time Random Walks (pp. 183-202)

E. Abad, S. B. Yuste and K. Lindenberg (Research Center on Dynamics of Solids, Voronezh State University of Architecture and Civil Engineering, Russia)

Chapter 9 – Exponential Integrators for Fractional Differential Equations (pp. 203-236)

Roberto Garrappa and Marina Popolizio (Institute of Mathematics and Computer Science, Jan Długosz University, Poland)

Chapter 10 – Non-Fragile Tuning of Fractional-Order PD Controllers for Integrating and Double Integrating Time-Delay Systems (pp. 237-256)

MirSaleh Bahavarnia and Mohammad Saleh Tavazoei (Electrical Engineering Department, Sharif University of Technology, Tehran, Iran)

Chapter 11 – On Discrete, Finite-Dimensional Approximation of Linear, Infinite Dimensional Systems (pp. 257-274)

Milan R. Rapaić, Tomislav B. Šekara and Mihailo P. Lazarević (GECAD, Portugal)

Index