Preface; Contents; List of Symbols; Fractional Differential Equations; 1.1 Definition of Euler Gamma Function and Its Properties; 1.2 Mittag-Leffler Function; 1.3 Definitions of Fractional Derivative-Integral; 1.4 Solutions of the Fractional State Equation of Continuous-Time Linear System; 1.5 Positivity of the Fractional Systems; 1.6 External Positivity of the Fractional Systems; 1.7 Positive Continuous-Time Linear Systems with Delays; 1.8 Positive Linear Systems Consisting of; Subsystems with Different Fractional Orders; 1.9 Descriptor Fractional Continuous-Time Linear Systems

1.10 Definition ofOrder Difference; 1.11 State Equations of the Discrete-Time Fractional Linear Systems; 1.12 Solution of the State Equations of the Fractional Discrete-Time Linear System; 1.13 Positive Fractional Linear Systems; 1.14 Externally Positive Fractional Systems; 1.15 Fractional Different Orders Discrete-Time Linear Systems; 1.16 Positive Fractional Different Orders Discrete-Time Linear Systems; 1.17 Descriptor Fractional Discrete-Time Linear Systems; Positive Fractional Electrical Circuits; 2.1 Fractional Electrical Circuits; 2.2 Positive Fractional Electrical Circuits

2.3 Analysis of the Fractional Electrical Circuits in Transient States2.4 Reciprocity Theorem for Fractional Circuits; 2.5 Equivalent Voltage Source Theorem and Equivalent Current Source Theorem; Descriptor Linear Electrical Circuits and Their Properties; 3.1 Descriptor Linear Electrical Circuits; 3.2 Descriptor Fractional Linear Electrical Circuits; 3.3 Polynomial Approach to Fractional Descriptor Electrical Circuits; 3.4 Positive Descriptor Fractional Electrical Circuits; Stability of Positive Standard Linear Electrical Circuits; 4.1 Stability of Positive Electrical Circuits

4.2 Positive UnstableElectrical Circuits; 4.3 Positive Unstable; Electrical Circuit; 4.4 Positive Unstable; Type Electrical Circuits; Reachability, Observability and Reconstructability of Fractional Positive Electrical Circuits and Their Decoupling Zeros; 5.1 Decomposition of the Pairs (; and (; of Linear Circuits; 5.2 Reachability of Positive Electrical Circuits; 5.3 Observability of Positive Electrical Circuits; 5.4 Constructability of Positive Electrical Circuits; 5.5 Decomposition of the Positive Pair; 5.6 Decomposition of the Positive Pair

5.7 Decoupling Zeros of the Positive Electrical Circuits5.8 Reachability of Positive Fractional Electrical Circuits; 5.9 Observability of Positive Fractional Electrical Circuits; Standard and Fractional Linear Circuits with Feedbacks; 6.1 Linear Dependence on Time of State Variable in Standard Electrical Circuits with State Feedbacks; 6.2 Zeroing of the State Vector of Standard Circuits by State-Feedbacks; 6.3 Zeroing of the State Vector of Standard Circuits by Output-Feedbacks; 6.4 Zeroing of the State Vector of Fractional Electrical Circuits by State-Feedbacks