Fractional calculus is now a well-established tool in engineering science, with very
promising applications in materials modelling. Indeed, several studies have shown that …

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 …

Mittag-Leffler Functions, Related Topics and Applications Page 1 Springer Monographs in
Mathematics Rudolf Gorenflo Anatoly A. Kilbas Francesco Mainardi Sergei Rogosin Mittag-Leffler …

In this paper we present an alternative representation of the diffusion equation and the
diffusion–advection equation using the fractional calculus approach, the spatial-time …

In this paper, we consider a boundary value problem for a nonlinear partial differential
equation of mixed type with Hilfer operator of fractional integro-differentiation in a positive …

In this work, we investigate a series of mathematical aspects for the fractional diffusion
equation with stochastic resetting. The stochastic resetting process in Evans–Majumdar …

Anomalous relaxation and diffusion processes have been widely quantified by fractional
derivative models, where the definition of the fractional-order derivative remains a historical …

This paper is devoted to proving the existence and uniqueness of solutions to Cauchy type
problems for fractional differential equations with composite fractional derivative operator on …

We discuss generalized integro-differential diffusion equations whose integral kernels are
not of a simple power law form, and thus these equations themselves do not belong to the …

Evolution systems containing fractional derivatives can result to suitable mathematical
models for describing better and important physical phenomena. In this paper, we consider …