TITLE:
Reconstruct the Heat Conduction Model with Memory Dependent Derivative
AUTHORS:
Wenwen Sun, Jinliang Wang
KEYWORDS:
Partial Differential Equation, Boundary Value Problem, Memory-Dependent Derivative (MDD), Caputo Type Fractional Derivative, Heat Conduction Equation
JOURNAL NAME:
Applied Mathematics,
Vol.9 No.9,
September
27,
2018
ABSTRACT: The classical heat conduction equation is derived from the assumption that
the temperature increases immediately after heat transfer, but the increase of
temperature is a slow process, so the memory-dependent heat conduction
model has been reconstructed. Numerical results show that the solution of
the initial boundary value problem of the new model is similar to that of the
classical heat conduction equation, but its propagation speed is slower than
that of the latter. In addition, the propagation speed of the former is also affected
by time delay and kernel function.