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 …

We consider anomalous stochastic processes based on the renewal continuous time
random walk model with different forms for the probability density of waiting times between …

This accessible monograph is devoted to a rapidly developing area on the research of
qualitative theory of fractional ordinary differential equations and evolution equations. It is …

We present a generalization of Hilfer derivatives in which Riemann–Liouville integrals are
replaced by more general Prabhakar integrals. We analyze and discuss its properties …

A system of fractional differential equations involving non-singular Mittag-Leffler kernel is
considered. This system is transformed to a type of weakly singular integral equations in …

We study distributed-order time fractional diffusion equations characterized by multifractal
memory kernels, in contrast to the simple power-law kernel of common time fractional …

Bessel and Mittag-Leffler functions are prominent within mathematical and scientific fields
due to increasing interest in non-conventional models within applied mathematics. Since the …

In this paper, a class of impulsive fractional Langevin equations is firstly offered. Formula of
solutions involving Mittag-Leffler functions and impulsive terms of such equations are …

Let us now consider the Fokker-Planck equation, which is a partial differential equation that
describes the time evolution of the PDF of the positions of particles, and was introduced in …

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