In this review paper, we are mainly concerned with the finite difference methods, the
Galerkin finite element methods, and the spectral methods for fractional partial differential …

Fractional calculus, which has two main features—singularity and nonlocality from its origin—
means integration and differentiation of any positive real order or even complex order. It has …

Fractional calculus, albeit a synonym of fractional integrals and derivatives which have two
main characteristics—singularity and nonlocality—has attracted increasing interest due to its …

This study focuses on the study of spatiotemporal and chaotic behavior in an extended non-
integer order dynamical systems which describe the spatial interaction between two …

This paper presents an iterative reproducing kernel algorithm for obtaining the numerical
solutions of Riesz fractional diffusion and advection-dispersion equations in porous media …

The fractional diffusion and dispersion equations are reinterpreted in determining the effect
of fluid flow and displacement processes through certain compressible phenomena and …

This paper is concerned with the construction and analysis of a novel linearized compact
ADI scheme for the two-dimensional Riesz space fractional nonlinear reaction–diffusion …

This paper focuses on studying Riesz derivative. An interesting investigation on properties of
Riesz derivative in one dimension indicates that it is distinct from other fractional derivatives …

The main objective in this paper is to propose an efficient numerical formulation for solving
the time-fractional distributed-order advection–diffusion equation. First, the distributed-order …

The main aim of the current paper is to propose an efficient numerical technique for solving
two-dimensional space-multi-time fractional Bloch–Torrey equations. The current research …