In this article, we present an efficient numerical algorithm, which combines the fourth-order
compact difference scheme (CDS) in space with the fast time two-mesh (TT-M) FBN-θ …

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 …

Fractional differential equation approach is frequently used to describe long-term
interactions in nonlinear systems. However, it results in difficulty in inverse problems as well …

The main focus of this study is to apply the two-step Adomian decomposition method
(TSADM) for finding a solution of a fractional-order non-linear differential equation by using …

In this paper, we mainly utilize a proper orthogonal decomposition (POD) to develop a highly
efficient reduced-order extrapolated finite difference (FD) algorithm for two-dimensional (2D) …

During this paper, a specific type of fractal-fractional diffusion equation is presented by
employing the fractal-fractional operator. We present a reliable and accurate operational …

In this paper, we investigate the existence and uniqueness of the multi-dimensional time-
space tempered fractional diffusion-wave (TSTFDW) equation by using the fixed point …

In this article, the 2D Chebyshev wavelets (CWs) are used for designing a proper procedure
to solve the variable-order (VO) fractional version of the nonlinear fourth-order diffusion …

In this article, we propose a second‐order shifted composite numerical integral formula,
which is denoted as the SCNIF2. We transform the nonlinear time fractional wave equation …

The main aim of this paper is to analyze the numerical method based upon the spectral
element technique for the numerical solution of the fractional advection-diffusion equation …