Abstract Models based on partial differential equations containing time–space fractional
derivatives have attracted considerable interest in the past decade because of their ability to …

In this article, a fast algorithm based on time two-mesh (TT-M) finite element (FE) scheme,
which aims at solving nonlinear problems quickly, is considered to numerically solve the …

In this article, three kinds of typical Caputo-type partial differential equations are numerically
studied via the finite difference methods/the local discontinuous Galerkin finite element …

In this paper, we study the magnetohydrodynamic (MHD) flow and heat transfer of the
fractional Jeffrey fluid in a straight channel, of which the cross section is a two-dimensional …

Calcium signaling in nerve cells is a crucial activity for the human brain to execute a diversity
of its functions. An alteration in the signaling process leads to cell death. To date, several …

In this paper, we propose a space–time finite element method for the multi-term time–space
fractional diffusion equation. First, some fractional derivative spaces are listed, some …

The transport of contaminants is a crucial environmental issue, and accurate modeling of
this phenomenon is vital for developing effective strategies for its management. In this study …

In recent years, the fractional differential equations have attracted a lot of attention due to
their interested characteristics. Meshfree methods are highly accurate and have been …

This work devotes to developing a systematic and convenient approach based on the
celebrated convolution quadrature theory to design and analyze difference formulas for …

In this article, a fast time two-mesh (TT-M) finite element (FE) method for the two-dimensional
space fractional Gray–Scott model is studied and discussed to get the numerical solutions …