Control of the transient subdiffusion exponent at short and long times

We consider a simple, physically and biologically motivated model of transient subdiffusion having different exponents in the mean squared displacement at short and long times. For this purpose, the sum of two independent stable processes (with different indexes) as subordinators is used. Based on their infinitely divisible properties, the probability density function of particle displacements and the Fokker-Planck-type equation are obtained. Manifesting different origins of inhomogeneities (traps) in the system, the subordinators' indexes affect the asymptotic behavior of the mean squared displacement for a particle walking in the environment. Links to the Jonscher universal relaxation law and the Prabhakar-type memory functions are given.