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

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.Comment: Keywords: Fractional derivative, anomalous heat diffusion, integral transform, analytical solutio

High-order Compact Difference Schemes for the Modified Anomalous Subdiffusion Equation

In this paper, two kinds of high-order compact finite difference schemes for second-order derivative are developed. Then a second-order numerical scheme for Riemann-Liouvile derivative is established based on fractional center difference operator. We apply these methods to fractional anomalous subdiffusion equation to construct two kinds of novel numerical schemes. The solvability, stability and convergence analysis of these difference schemes are studied by Fourier method in details. The convergence orders of these numerical schemes are $\mathcal {O}(\tau^2+h^6)$ and $\mathcal {O}(\tau^2+h^8)$, respectively. Finally, numerical experiments are displayed which are in line with the theoretical analysis.Comment: