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A new fractional derivative without singular kernel: Application to the modelling of the steady heat flow

Yang Xiao-Jun (China University of Mining and Technology, Department of Mathematics and Mechanics, Xuzhou, People's Republic of China)
Srivastava H.M. (University of Victoria, Department of Mathematics and Statistics, Victoria, British Columbia VW R, Canada + China Medical University, Taichung, Taiwan, ROC)
Machado Tenreiro J.A. (Polytechnic of Porto, Institute of Engineering, Department of Electrical Engineering, Porto, Portugal)

In this article we propose a new fractional derivative without singular kernel. We consider the potential application for modeling the steady heat-conduction problem. The analytical solution of the fractional-order heat flow is also obtained by means of the Laplace transform.

Keywords: heat conduction, steady heat flow, analytical solution, Laplace transform, fractional derivative without singular kernel