Time-fractional Caputo derivative versus other integrodifferential operators in generalized Fokker-Planck and generalized Langevin equations

Fractional diffusion and Fokker-Planck equations are widely used tools to describe anomalous in a large variety of complex systems. The equivalent formulations terms Caputo or Riemann-Liouville fractional derivatives can be derived as continuum limits continuous-time random walks associated with the Mittag-Leffler relaxation Fourier modes, interpolating between short-time stretched exponential long-time inverse power-law scaling. More recently, number other integrodifferential operators have been proposed, including Caputo-Fabrizio Atangana-Baleanu forms. Moreover, conformable derivative has introduced. We study here dynamics generalized from perspective moments, time-averaged mean-squared displacements, autocovariance functions. also Langevin based on these operators. differences different discussed compared dynamic behavior established models scaled Brownian motion motion. demonstrate that kernels not suitable introduced for physically relevant scenarios our paper. unveiled share similar properties motion, respectively.