We investigate the solutions of a generalized diffusion equation which extends some known equations such as the fractional diffusion equation and the porous medium equation. We start our study by considering the linear case and the nonlinear case afterward. The linear case is analyzed taking...

We investigate an N-dimensional fractional diffusion equation with radial symmetry by taking a spatial and time dependent diffusion coefficient into account, i.e., D˜(r,t)=D(t)r−η with D(t)=Dδ(t)+D¯(t). The equation is considered in a confined region and subjected to time dependent...

We investigate the solutions of a fractional diffusion equation with radial symmetry by using the Green function approach and by taking the N-dimensional case into account. In our analysis, a spatial time-dependent diffusion coefficient is considered, i.e., D(r,t)=Dtδ-1r-θ/Γ(α). The presence...

We analyze an anisotropic fractional diffusion equation that extends some known diffusion equations by considering a diffusion coefficient with spatial and time dependence, the presence of external forces and time fractional derivatives. We obtain new exact classes of solutions for a linear...

We devote this work to investigate the solutions of a generalized diffusion equation which contains spatial fractional derivatives and nonlinear terms. The presence of external forces and absorbent terms is also considered. The solutions found here can have a compact or long tail behavior and,...

We analyze a multidimensional nonlinear diffusion equation taking a spatial time dependent diffusion coefficient and external forces into account. We obtain new exact classes of solutions and investigate the transverse effects induced by an external force applied in the system. We also connect...

We analyse a N-dimensional anisotropic nonlinear Fokker–Planck equation by considering stationary and time-dependent solutions. The stationary solutions are obtained for very general situations, including those when the diffusion coefficients are spatial dependents. Time-dependent solutions...

We obtain new exact classes of solutions for the nonlinear fractional Fokker–Planck-like equation ∂tρ=∂x{D(x)∂μ−1xρν−F(x)ρ} by considering a diffusion coefficient D=D|x|−θ(θ∈R and D0) and a drift force F=−k1x+k̄γx|x|γ−1(k1,k̄γ,γ∈R). Connection with nonextensive...