TY - JOUR
TI - Diffusion models of heat and momentum with weakly singular kernels in the fading memories: How the integral-balance method can be applied?
AU - Hristov Jordan Y
JN - Thermal Science
PY - 2015
VL - 19
IS - 3
SP - 947
EP - 957
PT - Article
AB - This work presents an attempt to apply the heat-balance integral approach to  diffusion models with fading memories with weakly singular kernels resulting  in closed-form solutions. The main steps are exemplified by solutions where  the fading memory is represented by Volterra integrals and by a  time-fractional Riemann-Liouville derivative. The examples address sole  elastic (damping) effects and cases where the viscous diffusivity should be  taken into account. As examples polynomial approximation is applied,  demonstrating how to avoid problems in determination of the exponent of the  general parabolic profile, but without freedom to optimize the final  closed-form solution. In general, this is a new implementation of an old idea  and related methods to new models and we hope the demonstrated technique  could be useful in solutions of practical problems.