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Based on the processing of comments by users of online mass media to published news, changes in their emotional attitude to the events described were investigated. Time series of observed processes were obtained and analyzed. R/S analysis showed that the values of their Hirst coefficient are significantly different from 0.5, which shows that the structure of these series has fractality, and the processes described by it can have memory. Studies have shown that the magnitude of the expectation and variance of the amplitudes of users' emotional relationship to news depends on the time interval of their calculation ("sliding window") in a complex way (as the root of the fractional degree from the time interval). This suggests that the observed time series have fractality, and the processes themselves may have memory and a tendency to self-organize. Differential equations with partial fractional derivatives of the diffusion type can be used to take into account the effects of memory and self-organization. The fractional nature of the time derivatives of t, and the state variable x (the level value of the series) allows you to describe non-local processes in which the transition to a given state of the system (or process) depends not only on the local characteristics of the process in the vicinity of the point in question, but also on the entire range of values (memory). Non-locality in time can lead to self-organization. Existing solutions of the fractional-differential equation of the diffusion type consider cases when the value of the fractional derivative of the β in time lies in the 0<β≤1 range, and the value of the fractional derivative of the