In this paper, we consider a Riesz space-fractional reaction-dispersion equation (RSFRDE). The RSFRDE is obtained from the classical reaction-dispersion equation by replacing the second-order space derivative with a Riesz derivative of order β ∈ (1,2]. We propose an implicit finite difference approximation for RSFRDE. The stability and convergence of the finite difference approximations are ana...

The space-time-fractional diffusion equation with the Caputo time-fractional derivative and Riesz fractional Laplacian is considered in the case of axial symmetry. Mass absorption (mass release) is described by a source term proportional to concentration. The integral transform technique is used. Different particular cases of the solution are studied. The numerical results are illustrated graph...

This manuscript introduces a discrete technique to estimate the solution of double-fractional two-component Bose–Einstein condensate. The system consists two coupled nonlinear parabolic partial differential equations whose solutions are complex functions, and spatial fractional derivatives interpreted in Riesz sense. Initial homogeneous Dirichlet boundary data imposed on multidimensional domain...

A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. By the space-time fractional diffusion equation we mean an evolution equation obtained from the standard linear diffusion equation by replacing the second-order space derivative with a Riesz-Fell...

Derivatives and integrals of non-integer orders have a wide application to describe complex properties of physical systems and media including nonlocality of power-law type and long-term memory. We suggest an extension of the standard variational principle for fractional nonlocal media with power-law type nonlocality that is described by the Riesz-type derivatives of non-integer orders. As exam...

This work explores different particle-based approaches to the simulation of one-dimensional fractional sub-diffusion equations in unbounded domains. We rely on smooth particle approximations, and consider four methods for estimating the fractional diffusion term. The first method is based on a direct differentiation of the particle representation; it follows the Riesz definition of the fraction...

In this paper, a method for the digital simulation of wind velocity fields by Fractional Spectral Moment function is proposed. It is shown that by constructing a digital filter whose coefficients are the fractional spectral moments, it is possible to simulate samples of the target process as superposition of Riesz fractional derivatives of a Gaussian white noise processes. The key of this simul...

A model is considered for turbulent diffusion which consists of a Riesz space fractional derivative to describe the turbulent phenomenon and also includes advection and classical diffusion. We present a first order explicit numerical method and a second order implicit numerical method to solve our problem and prove convergence results for both methods, including the derivation of stability cons...

An extension of the general fractional calculus (GFC) is proposed as a generalization Riesz calculus, which was suggested by Marsel in 1949. The form GFC can be considered an from positive real line and Laplace convolution to m-dimensional Euclidean space Fourier convolution. To formulate form, Luchko approach construction GFC, Yuri 2021, used. integrals derivatives are defined convolution-type...

The maximum principle for the space and time-space fractional partial differential equations is still an open problem. In this paper, we consider a multi-term time-space Riesz-Caputo fractional differential equations over an open bounded domain. A maximum principle for the equation is proved. The uniqueness and continuous dependence of the solution are derived. Using a fractional predictor-corr...