Non integer order, state space model of heat transfer process using Atangana-Baleanu operator

Abstract

In the paper a new, state space, non integer order model of an one-dimensional heat transfer process is proposed. The model uses a new operator with Mittag-Leffler kernel, proposed by Atangana and Beleanu. The non integer order spatial derivative is expressed by Riesz operator. Analytical formula of the step response is given, the convergence of the model is discussed too. Theoretical results are verified by experiments.

Keywords

• non integer order systems
• heat transfer equation
• infinite dimensional systems
• fractional order state equation
• riesz operator
• caputo operator
• atangana-baleanu operator