In a simple preferential attachment network model, replacing the time derivative with a fractional-order derivative makes node activity peak and then decline, which the authors interpret as aging due to memory.
Holme, Network reachability of real-world contact sequences, Physical Review E 71 (4) (2005) 046119
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Memory effects on link formation in temporal networks: A fractional calculus approach
In a simple preferential attachment network model, replacing the time derivative with a fractional-order derivative makes node activity peak and then decline, which the authors interpret as aging due to memory.