title: General solution of the diffusion equation with a nonlocal diffusive term and a linear force term.
abstract: 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.
authors.affiliation: Universidade Estadual de Maringá, Departamento de Física, 87020-900 Maringá, Paraná, Brazil.
authors.forename: L C
authors.initials: LC
authors.lastname: Malacarne
authors.forename: R S
authors.initials: RS
authors.lastname: Mendes
authors.forename: E K
authors.initials: EK
authors.lastname: Lenzi
authors.forename: M K
authors.initials: MK
authors.lastname: Lenzi