References
- D. Cen and Z. Wang, Time two-grid technique combined with temporal second order difference method for two-dimensional semilinear fractional sub-diffusion equations, Appl. Math. Lett. 129 (2022), pp. 107919.
- D. Cen, Z. Wang, and Y. Mo, Second order difference schemes for time-fractional KdV-Burgers' equation with initial singularity, Appl. Math. Lett. 112 (2021), pp. 106829.
- D. Cen, Z. Wang, and Y. Mo, A fast compact difference scheme for the fourth-order multi-term fractional sub-diffusion equation with non-smooth solution, Filomat. 35 (2021), pp. 1495–1509.
- L. Feng, F. Liu, and I. Turner, Finite difference/finite element method for a novel 2D multi-term time-fractional mixed sub-diffusion and diffusion-wave equation on convex domains, Commun. Nonlinear Sci. Numer. Simulat. 70 (2019), pp. 354–371.
- G. Gao, A. Alikhanov, and Z. Sun, The temporal second order difference schemes based on the interpolation approximation for solving the time multi-term and distributed-order fractional sub-diffusion equations, J. Sci. Comput. 73 (2017), pp. 93–121.
- E. Hesameddini, A. Rahimi, and E. Asadollahifard, On the convergence of a new reliable algorithm for solving multi-order fractional differential equations, Commun. Nonlinear Sci. Numer. Simulat. 34 (2016), pp. 154–164.
- C. Ji, Z. Sun, and Z. Hao, Numerical algorithms with high spatial accuracy for the fourth-order fractional sub-diffusion equations with the first Dirichlet boundary conditions, J. Sci. Comput. 66 (2016), pp. 1148–1174.
- S. Jiang, J. Zhang, Q. Zhang, and Z. Zhang, Fast evalution of the Caputo fractional derivative and its applications to fractional diffusion equations, Commun. Comput. Phys. 21 (2017), pp. 650–678.
- B. Jin, R. Lazarov, Y. Liu, and Z. Zhou, The Galerkin finite element method for a multi-term time-fractional diffusion equation, J. Comput. Phys. 281 (2015), pp. 825–843.
- B. Jin, R. Lazarov, and Z. Zhou, An analysis of the L1 scheme for the subdiffusion equation with nonsmooth data, IMA J. Numer. Anal. 36 (2016), pp. 197–221.
- V. Karpman, Stabilization of soliton instabilities by higher-order dispersion: fourth order nonlinear Schrödinger-type equations, Phys. Rev. E. 53 (1996), pp. 1336–1339.
- N. Kopteva, Error analysis of the L1 method on graded and uniform meshes for a fractional-derivative problem in two and three dimensions, Math. Comput. 88 (2019), pp. 2135–2155.
- C. Li, Q. Yi, and A. Chen, Finite difference methods with non-uniform meshes for nonlinear fractional differential equations, J. Comput. Phys. 316 (2016), pp. 614–631.
- D. Li, J. Zhang, and Z. Zhang, Unconditionally optimal error estimates of a linearized galerkin method for nonlinear time fractional reaction-subdiffusion equations, J. Sci. Comput. 76 (2018), pp. 848–866.
- H. Liao, D. Li, and J. Zhang, Sharp error estimate of the nonuniform L1 formula for linear reaction-subdiffusion equations, SIAM J. Numer. Anal. 56 (2018), pp. 1112–1133.
- H. Liao, W. Mclean, and J. Zhang, A discrete Grönwall inequality with applications to numerical schemes for subdiffusion problems, SIAM J. Numer. Anal. 57 (2019), pp. 218–237.
- H. Liao, Y. Yan, and J. Zhang, Unconditional convergence of a fast two-level linearized algorithm for semilinear subdiffusion equations, J. Sci. Comput. 80 (2019), pp. 1–25.
- F. Liu, M. Meerschaert, R. McGough, P. Zhuang, and Q. Liu, Numerical methods for solving the multi-term time-fractional wave-diffusion equation, Fract. Calc. Appl. Anal. 16 (2013), pp. 9–25.
- P. Lyu, Y. Liang, and Z. Wang, A fast linearized finite difference method for the nonlinear multi-term time-fractional wave equation, Appl. Numer. Math. 151 (2020), pp. 448–471.
- K. Oldhan and J. Spainer, The Fractional Calculus, Academic Press, New York, 1974.
- C. Ou, D. Cen, S. Vong, and Z. Wang, Mathematical analysis and numerical methods for Caputo-Hadamard fractional diffusion-wave equations, Appl. Numer. Math. 177 (2022), pp. 34–57.
- L. Qiao, Z. Wang, and D. Xu, An alternating direction implicit orthogonal spline collocation method for the two dimensional multi-term time fractional integro-differential equation, Appl. Numer. Math.151 (2020), pp. 199–212.
- M. Ran and C. Zhang, New compact difference scheme for solving the fourth-order time fractional sub-diffusion equation of the distributed order, Appl. Numer. Math. 129 (2018), pp. 58–70.
- J. Shen, Z. Sun, and R. Du, Fast finite difference schemes for the time-fractional diffusion equations with a weak singularity at the initial time, East Asian J. Appl. Math. 8 (2018), pp. 834–858.
- I. Sneddon, Fourier Transforms, McGraw Hill, New York, 1951.
- M. Stynes, E. O'Riordan, and J. Gracia, Error analysis of a finite difference method on graded meshes for a time-fractional diffusion equation, SIAM J. Numer. Anal. 55 (2017), pp. 1057–1079.
- H. Sun, X. Zhao, and Z. Sun, The temporal second order difference schemes based on the interpolation approximation for the time multi-term fractional wave equation, J. Sci. Comput. 78 (2019), pp. 467–498.
- S. Vong and Z. Wang, Compact finite difference scheme for the fourth-order fractional subdiffusion system, Adv. Appl. Math. Mech. 6 (2014), pp. 419–435.
- Z. Wang, C. Ou, and S. Vong, A second-order scheme with nonuniform time grids for Caputo-Hadamard fractional sub-diffusion equations, J. Comput. Appl. Math. 414 (2022), pp. 114448.
- H. Wang, D. Yang, and S. Zhu, Accuracy of finite element methods for boundary-value problems of steady-state fractional diffusion equations, J. Sci. Comput. 70 (2017), pp. 429–449.
- X. Yang, H. Zhang, and D. Xu, Orthogonal spline collocation method for the fourth-order diffusion system, Comput. Math. Appl. 75 (2018), pp. 3172–3185.
- Z. Yao and Z. Wang, A compact difference scheme for fourth-order fractional subdiffusion equations with Neumann boundary conditions, J. Appl. Anal. Comput. 8 (2018), pp. 1159–1169.
- F. Zeng, Z. Zhang, and G. Karniadakis, Second-order numerical methods for multi-term fractional differential equations: smooth and non-smooth solutions, Comput. Methods Appl. Mech. Engrg. 327 (2017), pp. 478–502.
- P. Zhang and H. Pu, A second-order compact difference scheme for the fourth-order fractional sub-diffusion equation, Numer. Algor. 76 (2017), pp. 573–598.