Memory-Dependent Derivative Versus Fractional Derivative (IV): Space-Dependent Derivative for Unsteady Heat Diffusion

In recent decades, the fractional derivative (FD) and memory-dependent derivative (MDD) have been borrowed for modifying the unsteady diffusion process. Yet, according to their definitions, only memory effects in temporal sense are reflected. To make spatial modifications, that is, a new version of MDD, the space-dependent derivative (SDD) is developed here. With the help of it, the heat diffusion process is remodeled in a more objective manner. The comparisons among the conventional model, spatial FD model, and SDD model show that the last one has the most expressive force, and it can be borrowed for considering other unsteady diffusion problems.