Analysis, Modeling and Stability of Fractional Order Differential Systems 1

This book introduces an original fractional calculus methodology (‘the infinite state approach’) which is applied to the modeling of fractional order differential equations (FDEs) and systems (FDSs). Its modeling is based on the frequency distributed fractional integrator, while the resulting model corresponds to an integer order and infinite dimension state space representation. This original modeling allows the theoretical concepts of integer order systems to be generalized to fractional systems, with a particular emphasis on a convolution formulation.

1. The Fractional Integrator. 2. Frequency Approach to the Synthesis of the Fractional Integrator. 3. Comparison of Two Simulation Techniques. 4. Fractional Modeling of the Diffusive Interface. 5. Modeling of Physical Systems with Fractional Models: an Illustrative Example. 6. The Distributed Model of the Fractional Integrator. 7. Modeling of FDEs and FDSs. 8. Fractional Differentiation. 9. Analytical Expressions of FDS Transients. 10. Infinite State and Fractional Differentiation of Functions.