General solution of the diffusion equation with a nonlocal diffusive term and a linear force term.
We obtain a formal solution for a large class of diffusion equations with a spatial kernel dependence in the diffusive term. The presence of this kernel represents a nonlocal dependence of the diffusive process and, by a suitable choice, it has the spatial fractional diffusion equations as a particular case. We also consider the presence of a linear external force and source terms. In addition, we show that a rich class of anomalous diffusion, e.g., the Lévy superdiffusion, can be obtained by an appropriated choice of kernel.
Malacarne
L C
LC
Universidade Estadual de Maringá, Departamento de Física, 87020-900 Maringá, Paraná, Brazil.
Mendes
R S
RS
Lenzi
E K
EK
Lenzi
M K
MK