[1] Abbaszadeh, M., Dehghan, M.: Meshless upwind local radial basis function-finite difference technique to simulate the time-fractional distributed-order advection-diffusion equation. Eng. Comput. 37, 873-889 (2021)
[2] Bu, W., Ji, L., Tang, Y., Zhou, J.: Space-time finite element method for the distributed-order time fractional reaction diffusion equations. Appl. Numer. Math. 152, 446-465 (2020)
[3] Chechkin, A.V., Gorenflo, R., Sokolov, I.M.: Retarding subdiffusion and accelerating superdiffusion governed by distributed-order fractional diffusion equations. Phys. Rev. E 66(4), 046129 (2002)
[4] Choudhary, R., Singh, S., Kumar, D.: A higher order unconditionally stable numerical technique for multi-term time-fractional diffusion and advection-diffusion equations. Comput. Appl. Math. 43(5), 303 (2024)
[5] Dahlquist, G., Björck, Å.: Numerical Methods in Scientific Computing, vol. I. Society for Industrial and Applied Mathematics, Providence (2008)
[6] Derakhshan, M.H., Rezaei, H., Marasi, H.R.: An efficient numerical method for the distributed order time-fractional diffusion equation with error analysis and stability. Math. Comput. Simul. 214, 315-333 (2023)
[7] Guo, S., Chen, Y., Mei, L., Song, Y.: Finite difference/generalized Hermite spectral method for the distributed-order time-fractional reaction-diffusion equation on multi-dimensional unbounded domains. Comput. Math. Appl. 93, 1-19 (2021)
[8] Holte, J.M.: Discrete Grönwall lemma and applications. In: MAA-NCS Meeting at the University of North Dakota, vol. 24, pp. 1-7 (2009)
[9] Hu, J.H., Wang, J.G., Nie, Y.F.: Two high-order difference schemes for solving time distributed-order diffusion equations. Appl. Math. Mech. 40(7), 791-800 (2019)
[10] Huang, C., Chen, H., An, N.: \beta-robust superconvergent analysis of a finite element method for the distributed order time-fractional diffusion equation. J. Sci. Comput. 90(1), 44 (2022)
[11] Irandoust-Pakchin, S., Hossein Derakhshan, M., Rezapour, S., Adel, M.: An efficient numerical method for the distributed-order time-fractional diffusion equation with the error analysis and stability properties. Math. Methods Appl. Sci. 48(3), 2743-2765 (2025)
[12] Li, L., Chen, Z., Du, H., Jiang, W., Zhang, B.: A meshless approach based on fractional interpolation theory and improved neural network bases for solving non-smooth solution of 2D fractional reaction-diffusion equation with distributed order. Commun. Nonlinear Sci. Numer. Simul. 138, 108245 (2024)
[13] Li, X., Rui, H.: Two temporal second-order H^1-Galerkin mixed finite element schemes for distributed-order fractional sub-diffusion equations. Numer. Algorithms 79(4), 1107-1130 (2018)
[14] Liu, L., Chen, S., Feng, L., Zhu, J., Zhang, J., Zheng, L., Xie, C.: A novel distributed order time fractional model for heat conduction, anomalous diffusion, and viscoelastic flow problems. Comput. Fluids 265, 105991 (2023)
[15] Liu, Q., Mu, S., Liu, Q., Liu, B., Bi, X., Zhuang, P., Li, B., Gao, J.: An RBF based meshless method for the distributed order time fractional advection-diffusion equation. Eng. Anal. Bound. Elem. 96, 55-63 (2018)
[16] Mokhtari, R., Mostajeran, F.: A high order formula to approximate the Caputo fractional derivative. Commun. Appl. Math. Comput. 2(1), 1-29 (2020)
[17] Ramezani, M., Mohammadi, M., Mokhtari, R.: dPINNs: Distributed-Order Physics-Informed Neural Networks (Under review)
[18] Ramezani, M., Mokhtari, R.: A novel high-order finite-difference method for the time-fractional diffusion equation with smooth/nonsmooth solutions. Bull. Iran. Math. Soc. 48(6), 3987-4013 (2022)
[19] Ramezani, M., Mokhtari, R., Haase, G.: Analysis of stability and convergence for L-type formulas combined with a spatial finite element method for solving subdiffusion problems. Electron. Trans. Numer. Anal. 55, 568-584 (2022)
[20] Ramezani, M., Mokhtari, R., Yan, Y.: Correction of a high-order numerical method for approximating time-fractional wave equation. J. Sci. Comput. 100(3), 71 (2024)
[21] Ren, J., Chen, H.: A numerical method for distributed order time fractional diffusion equation with weakly singular solutions. Appl. Math. Lett. 96, 159-165 (2019)
[22] Suliman, M., Ibrahim, M., Algehyne, E.A., Ali, V.: A study of an efficient numerical method for solving the generalized fractional reaction-diffusion model involving a distributed-order operator along with stability analysis. Comput. Math. Appl. 180, 61-75 (2025)
[23] Sun, L.Y., Fang, Z.W., Lei, S.L., Sun, H.W., Zhang, J.L.: A fast algorithm for two-dimensional distributed-order time-space fractional diffusion equations. Appl. Math. Comput. 425, 127095 (2022)
[24] Sun, L.Y., Lei, S.L., Sun, H.W., Zhang, J.L.: An α-robust fast algorithm for distributed-order time-space fractional diffusion equation with weakly singular solution. Math. Comput. Simul. 207, 437-452 (2023)
[25] Wei, L., Liu, L., Sun, H.: Stability and convergence of a local discontinuous Galerkin method for the fractional diffusion equation with distributed order. J. Appl. Math. Comput. 59, 323-341 (2019)
[26] Wen, C., Wang, J., Liu, Y., Li, H., Fang, Z.: Unconditionally optimal time two-mesh mixed finite element algorithm for a nonlinear fourth-order distributed-order time fractional diffusion equation. Physica D 460, 134090 (2024)
[27] Yang, X., Zhang, H., Xu, D.: WSGD-OSC scheme for two-dimensional distributed order fractional reaction-diffusion equation. J. Sci. Comput. 76(3), 1502-1520 (2018)
[28] Yang, Z., Zheng, X., Wang, H.: A variably distributed-order time-fractional diffusion equation: analysis and approximation. Comput. Methods Appl. Mech. Eng. 367, 113118 (2020)
