MODELLING ANOMALOUS TRANSPORT WITH EXTERNAL FIELD BY INTEGRATED SUBORDINATED BROWNIAN MOTION

We consider a new type of anomalous transport in the particular type of continuous time random walk (CTRW) in the stochastic process where the particle have interaction with its environment and may behave unexpectedly more random or more stable. The process that was utilized in this study uses the integrated Brownian motion subordinated by an inverse α-stable subordinator. The proposed new process has external field which causes the two most probable points to have another point between them and we termed it as anomalous jump. We compute the time-scale for the mean squared displacement of the usual continuous time random walk (CTRW) and the anomalous jump. Furthermore, as expected, the time scale for the anomalous jump exhibits an interaction with its environment when there is an imposed memory kernel function. Lastly, using the time scale obtained for the MSD of the anomalous jump, we have generalized the external drift force field on the coupled Langevin equation obtained by Fogedby