A fractional derivative with two singular kernels and application to a heat conduction problem

[摘要] In this article, we suggest a new notion of fractional derivative involving two singular kernels. Some properties related to this new operator are established and some examples are provided. We also present some applications to fractional differential equations and propose a numerical algorithm based on a Picard iteration for approximating the solutions. Finally, an application to a heat conduction problem is given.

[学科分类] 航空航天科学

[关键词] Fractional derivative;Two singular kernels;Picard iteration;Heat conduction problem