Fractional difference/finite element approximations for the time–space fractional telegraph equation

Fractional Difference Approximations for Time-Fractional Telegraph Equation

“…Actually, some authors have already studied the numerical solutions to some kinds of time or space fractional telegraph equations, such as C. Li [14], Z. Zhao [15], N. J. Ford [16], A. Sevimlican [17], and M. Dehghan [18]. The fractional telegraph equation we consider here is different from all of which they discussed in their papers.…”

An $$H^1$$ H 1 -Galerkin mixed finite element method for time fractional reaction–diffusion equation

“…In the near future, we will study the H 1 -Galerkin MFE method to solve the fractional telegraph equation [7], the variable-order fractional advection diffusion equation [10] and so on. At the same time, we are trying to find some new discrete methods for approximating fractional derivatives and study some other MFE procedures [37,42] based on moving finite element method [1] for solving the fractional PDEs.…”

“…Generally, the fractional partial differential equations (PDEs) can be grouped into three categories: time fractional PDEs [1][2][3], space fractional PDEs [4][5][6] and spacetime fractional PDEs [7]. Recently, more and more efficient numerical methods, such as finite difference methods [4,[8][9][10][11][12][13][14][15][16][17][18][19][20][21], finite element methods [1][2][3]22,23], spectral methods [24] and LDG methods [25,26], have been found and studied for fractional PDEs.…”

An approximate solution to a moving boundary problem with space–time fractional derivative in fluvio-deltaic sedimentation process

“…Voller [13] presented fractional (non-integer) form of a limit Stefan problem using Caputo derivatives for both space and time, and discussed exact solution of the problem. Recently, some researchers [14][15][16][17] also discussed various mathematical models governed with different fractional derivatives for both the space and time.…”