Eur. Phys. J. Special Topics 226, 3567–3575 (2017)
https://doi.org/10.1140/epjst/e2018-00020-2

Regular Article

A new fractional derivative involving the normalized sinc function without singular kernel

¹ State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, P.R. China
² School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, P.R. China
³ Institute of Engineering, Polytechnic of Porto, Department of Electrical Engineering, Rua Dr. António Bernardino de Almeida, 4249-015 Porto, Portugal
⁴ Department of Mathematics, Cankya University, Ogretmenler Cad. 14, Balgat 06530, Ankara, Turkey
⁵ Institute of Space Sciences, Magurele, Bucharest, Romania

Received: 27 May 2017
Received in final form: 22 October 2017
Published online: 25 July 2018

Abstract

In this paper, a new fractional derivative involving the normalized sinc function without singular kernel is proposed. The Laplace transform is used to find the analytical solution of the anomalous heat-diffusion problems. The comparative results between classical and fractional-order operators are presented. The results are significant in the analysis of one-dimensional anomalous heat-transfer problems.