Distributed-order fractional calculus (DOFC) is a rapidly emerging branch of the broader
area of fractional calculus that has important and far-reaching applications for the modeling …

We obtain a generalized diffusion equation in modified or Riemann-Liouville form from
continuous time random walk theory. The waiting time probability density function and mean …

Classical option pricing schemes assume that the value of a financial asset follows a
geometric Brownian motion (GBM). However, a growing body of studies suggest that a …

Generalized (non-Markovian) diffusion equations with different memory kernels and
subordination schemes based on random time change in the Brownian diffusion process are …

Jeffreys equation provides an increasingly popular extension of the diffusive laws of Fourier
and Fick for heat and particle transport. Similar to generalisations of the diffusion equation …

We consider a generalized Langevin equation with regularized Prabhakar derivative
operator. We analyze the mean square displacement, time-dependent diffusion coefficient …

The diffusion equation with a general convolutional derivative in time is considered on a
bounded domain, as one of the boundary conditions is nonlocal. We are concerned with the …

We address the effect of stochastic resetting on diffusion and subdiffusion process. For
diffusion we find that mean square displacement relaxes to a constant only when the …

The concept of subordination, originally introduced in the probability and stochastic
processes theories, has also appeared in analysis of evolution equations. So it is not …

The Cattaneo or telegrapher's equation describes the crossover from initial ballistic to
normal diffusion. Here we study and survey time-fractional generalisations of this equation …