A Time-Fractional Diffusion Equation with Generalized Memory Kernel in Differential and Difference Settings with Smooth Solutions

作者：Alikhanov Anatoly A

来源：Computational Methods in Applied Mathematics, 2017, 17(4): 647-660.

DOI：10.1515/cmam-2017-0035

<jats:title>Abstract</jats:title><jats:p>In this paper, an a priori estimate for the corresponding differential problem is obtained by using the method of the energy inequalities. We construct a difference analog of the Caputo fractional derivative with generalized memory kernel (L1 formula). The basic properties of this difference operator are investigated and on its basis some difference schemes generating approximations of the second and fourth order in space and the</jats:p>

• 出版日期2017-10