Numerical approximation of nonlinear fractional differential equations with subdiffusion and superdiffusion

On the existence of solutions of fractional integro-differential equations

“…Furthermore, several analytical and numerical methods have been proposed for approximate solutions of fractional differential equations, e.g. [8,20,23,29,31,33,38].…”

Space-dependent source determination in a time-fractional diffusion equation using a local discontinuous Galerkin method

“…A time-fractional diffusion equation occurs when replacing the standard time derivative with a time fractional derivative and can be applied in modeling of some problems in porous flows, rheology and mechanical systems, models of a variety of biological processes, control and robotics, transport in fusion plasmas, and many other areas of applications. The direct problems corresponding to the time-fractional diffusion equations have been studied extensively in recent years, including uniqueness and existence results [2], some analytical or numerical solutions [13,7,31], and numerical methods such as finite element methods or finite difference methods [12,14]. Here, we focus on an interesting inverse problem defined to the fractional inverse problem pioneered by Murio [18,16,17].…”

“…, M be the mesh points. The time fractional derivative (1.3) is approximated by a simple quadrature formula known as the L1 rule [13],…”

Numerical study of time-fractional hyperbolic partial differential equations

“…The numerical solution of partial differential equations with sub and super diffusion is proposed by Li et al [16] . Wei et al [28] proposed the numerical solution of fractional telegraph equation.…”