This article proposes a time fractional dual-phase-lagging (DPL) heat conduction model in a
double-layered nanoscale thin film with the temperature-jump boundary condition and a
thermal lagging effect interfacial condition between layers. The model is proved to be well-
posed. A finite difference scheme with second-order spatial convergence accuracy in
maximum norm is then presented for solving the fractional DPL model. Unconditional
stability and convergence of the scheme are proved by using the discrete energy method. A …

This article proposes a new nanoscale heat transfer model based on the Caputo type
fractional dual-phase-lagging (DPL) heat conduction equation with the temperature-jump
boundary condition. The model is proved to be well-posed. A finite difference scheme based
on the L1 approximation for the Caputo derivative is then presented for solving the fractional
DPL model. Unconditional stability and convergence of the scheme are proved by using the
discrete energy method. Three numerical examples are given to verify the accuracy of the …