doiSerbia

A new general fractional-order derivataive with Rabotnov fractional-exponential kernel applied to model the anomalous heat transfer

Yang Xiao-Jun (State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou, China)
Abdel-Aty Mahmoud (Center for Photonics and Smart Materials (CPSM), Zewail City of Science and Technology, Egypt + Mathematics Department, Faculty of Sciences, Sohag University, Egypt + Applied Science University, Kingdom of Bahrain)
Cattani Carlo (Engineering School, DEIM, University of Tuscia, Viterbo, Italy + Ton Duc Thang University, HCMC, Vietnam)

In this paper, we consider a general fractional-order derivataive of the Liouville-Caputo type with the non-singular kernel of the Rabotnov fractional-exponential function for the first time. A new general fractional-order derivataive heat transfer model is discussed in detail. The general fractional-order derivataive formula is a new mathematical tool proposed to model the anomalous behaviors in complex and power-law phenomena.

Keywords: power law Rabotnov fractional exponential function, general fractional-order derivataive, heat transfer, non-singular kernel