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

Thermal Science

Abdel-Aty Mahmoud¹  Cattani Carlo²  Yang Xiao-Jun³ 

[1] 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;Engineering School, DEIM, University of Tuscia, Viterbo, Italy + Ton Duc Thang University, HCMC, Vietnam;State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou, China;

关键词: power law Rabotnov fractional exponential function;    general fractional-order derivataive;    heat transfer;    non-singular kernel;   

DOI  :  10.2298/TSCI180320239Y

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown