Partial differential equations (PDEs) are used with huge success to model phenomena
across all scientific and engineering disciplines. However, across an equally wide swath …

This review article aims to stress and reunite some of the analytic formalism of the
anomalous diffusive processes that have succeeded in their description. Also, it has the …

Nonlocal and fractional-order models capture effects that classical partial differential
equations cannot describe; for this reason, they are suitable for a broad class of engineering …

The prime aim of the present paper is to continue develo** the theory of tempered
fractional integrals and derivatives of a function with respect to another function. This theory …

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 boundary value problem in weak form of a steady-state Riesz space-
fractional diffusion equation (FDE) of order 2-α with 0<α<1. By using a finite volume …

In this paper, we first construct an appropriate new generating function, and then based on
this function, we establish a fourth-order numerical differential formula approximating the …

Fractional diffusion equations (FDEs) are a mathematical tool used for describing some
special diffusion phenomena arising in many different applications like porous media and …

We propose a local modification of the standard subdiffusion model by introducing the initial
Fickian diffusion, which results in a multiscale diffusion model. The developed model …

This paper develops appropriate boundary conditions for the two-sided fractional diffusion
equation, where the usual second derivative in space is replaced by a weighted average of …