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

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.

Keywords: Fractional derivative, anomalous heat diffusion, integral transform, analytical solution