Fractional discrete-continuous model of heat transfer process

Abstract

The paper proposes a new, state space, finite dimensional, fractional order model of a heat transfer in one dimensional body. The time derivative is described by Caputo operator. The second order central difference describes the derivative along the length. The analytical formulae of the model responses are proved. The stability, convergence, and positivity of the model are also discussed. Theoretical results are verified by experiments.

Keywords

• non integer order systems
• heat transfer equation
• finite difference
• caputo operator
• positive systems