In this paper, we consider an orthogonal spline collocation (OSC) method to solve the fourth-
order multi-term subdiffusion equation. The L1 method on graded meshes is employed in …

Starting with an introduction to fractional derivatives and numerical approximations, this
book presents finite difference methods for fractional differential equations, including time …

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 work, we consider two of the most frequently used two-dimensional nonlinear time-
fractional anomalous sub-diffusion models for simulating transport phenomena in …

The current manuscript introduces a novel numerical treatment for multi-term fractional
differential equations with variable coefficients. The spectral Galerkin approach is developed …

In previous study on the flow of fractional viscoelastic fluid between two coaxial cylinders,
due to the complexity of computation, researchers commonly assume that the flow area is a …

Recently, numerous numerical schemes have been developed for solving single-term time-
space fractional diffusion-wave equations. Among them, some popular methods were …

In this article, a time two-mesh (TT-M) algorithm combined with the H 1-Galerkin mixed finite
element (FE) method is introduced to numerically solve the nonlinear distributed-order sub …

A family of novel time-stepping methods for the fractional calculus operators is presented
with a shifted parameter. The truncation error with second-order accuracy is proved under …

The paper aims to put forth a radial basis function-based meshless approach for the
numerical solution of the time-fractional nonlinear mixed diffusion and diffusion-wave …