Wang, J.L. and Li, H.F. (2011) Surpassing the Fractional Derivative: Concept of the Memory-Dependent Derivative. Computers and Mathematics with Applications, 62, 1562-1567.
https://doi.org/10.1016/j.camwa.2011.04.028

has been cited by the following article:

• 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.