Correlation function induced by a generalized diffusion equation with the presence of a harmonic potential

•Calculation of the correlation function.•The correlation function is connected to the survival probability.•The model can be applied to the internal dynamics of proteins.

An integro-differential diffusion equation with linear force, based on the continuous time random walk model, is considered. The equation generalizes the ordinary and fractional diffusion equations, which includes short, intermediate and long-time memory effects described by the waiting time probability density function. Analytical expression for the correlation function is obtained and analyzed, which can be used to describe, for instance, internal motions of proteins. The result shows that the generalized diffusion equation has a broad application and it may be used to describe different kinds of systems.