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Abstract

We consider a shear-driven anomalous diffusion by introducing a memory kernel in the Fokker–Planck equation, which results from the long-tailed waiting time of the particle. We analyze the probability density function and the corresponding moments in the framework of the subordination approach. The moments, obtained analytically, show that the system exhibits characteristic crossover anomalous dynamics. We also explore corresponding process under stochastic resetting, and we find that the system reaches a non-equilibrium stationary state in the long time limit that also results in saturation of the evolution of corresponding mean squared displacement, variance, skewness, and kurtosis.