Diffusion models with weakly singular kernels in the fading memories how the integral-balance method can be applied?
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2015-01-01
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Abstract
This work presents an attempt to apply the integral-balance approach to diffusion models with fading memories expressed by weakly singular kernels. It demonstrates how three integration techniques (heat-balance integral method, double-integration method, and frozen front approach) work with a general parabolic profile with unspecified exponent and result 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.