[1] Adebisi, A.F., Gbolagade, G.M., Ogunniran, M.O. and Ajewole, K.P. Convergence and
stability analysis of finite difference methods, Caputo derivatives, and collocation methods
applied to space fractional diffusion equations, Proc. Int. Conf. on Science, Engineering and
Business for Driving Sustainable Development Goals (SEB4SDG 2024), 2024.
[2] Adel, M. Numerical simulations for the variable order two-dimensional reaction sub-diffusion
equation: linear and nonlinear, Fractals, 2022.
[3] Baeumer, B., Kovács, M. and Meerschaert, M.M. Numerical solutions for fractional reaction-
diffusion equations, Comput. Math. Appl., 55 (10) (2008), 2212–2226.
[4] Cho, H., Venturi, D. and Karniadakis, G.E. Karhunen-Loève expansion for multi-correlated
stochastic processes, Probabilist. Eng. Mech., 34 (2013), 157–167.
[5] Chow, W.C. Brownian bridge, Wiley Interdiscip. Rev.: Comput. Stat., 1 (3) (2009), 362–
367.
[6] Dos Santos, M.A.F. Fractional Prabhakar derivative in diffusion equation with non-static
stochastic resetting, Physics (Switzerland), 1 (2) (2019), 288–302.
[7] Goulart, A.G.O., Lazo, M.J., Suarez, J.M.S. and Moreira, D.M. Fractional derivative models
for atmospheric dispersion of pollutants, Physica A, 477 (2017), 9–19.
[8] Guo, B., Pu, X. and Huang, F. Fractional partial differential equations and their numerical
solutions, World Scientific, Singapore, 2015.
[9] Hamrouni, W. and Abdennadher, A. Random walk’s models for fractional diffusion equation,
Discrete Contin. Dyn. Syst. Ser. B, 21(10) (2016), 3339–3356.
[10] Hernandez-Martinez, E., Valdés-Parada, F., Alvarez-Ramirez, J. and Morales-Zarate, E.
A Green’s function approach for the numerical solution of a class of fractional reaction-
diffusion equations, Math. Comput. Simul., 120 (2016), 36–52.
[11] Ju, Y., Yang, J., Liu, Z. and Xu, Q. Meshfree methods for the variable-order fractional
advection-diffusion equation, Math. Comput. Simul., 217 (2023), 287–300.
[12] Kim, M., Mert Coskun, O., Ordu, S. and Mutlu, R. Modeling pollutant diffusion in the
ground using conformable fractional derivative in spherical coordinates with complete sym-
metry, Symmetry, 16 (2024), 427.
[13] Kundu, A., Bernardin, C., Saito, K. and Dhar, A. Fractional equation description of an open
anomalous heat conduction set-up, J. Stat. Mech. Theory Exp., 2019(1) (2019), 013203.
[14] Lord, G.J., Powell, C.E. and Shardlow, T. An introduction to computational stochastic
PDEs, Cambridge University Press, 2014.
[15] Mohammed, W.W., Alshammari, M., Cesarano, C. and El-Morshedy, M. Brownian mo-
tion effects on the stabilization of stochastic solutions to fractional diffusion equations with
polynomials, Mathematics, 10 (3) (2022), 359.
[16] Moghaddam, B.P., Zaky, M.A., Lopes, A.M. and Galhano, A. A Fractional time-space
stochastic advection-diffusion equation for modeling atmospheric moisture transport at
ocean-atmosphere interfaces, Fractal Fract., 8 (2024), 163.
[17] Moghaddam, B.P., Babaei, A., Dabiri, A. and Galhano, A. Fractional stochastic partial
differential equations: Numerical advances and practical applications—A state of the art
review, Symmetry, 16 (2024), 257.
[18] Moniri, Z., Babaei, A. and Moghaddam, B.P. Robust numerical framework for simulating 2D
fractional time–space stochastic diffusion equation driven by spatio-temporal noise: L1-FFT
hybrid approach, Commun. Nonlinear Sci. Numer. Simul., 136 (2025), 109612.
[19] Noor, S., Alrowaily, A.W., Alqudah, M. and El-Tantawy, S.A. Innovative solutions to the
fractional diffusion equation using the Elzaki transform, Math. Comput. Appl., 29 (1) (2024),
7.
[20] Poirion, F. and Zentner, I. Non-Gaussian non-stationary models for natural hazard modeling,
Appl. Math. Model., 37 (1-2) (2013), 533–546.
[21] Poirion, F. and Zentner, I. Stochastic model construction of natural hazards given experi-
mental measures, Proc. 11th Int. Conf. on Structural Safety and Reliability (ICOSSAR),
2013.
[22] Qu, B., Addison, P.S. and Dong, Y. Fractal simulation of diffusion of pollutants in open
ocean, Adv. Sci. Technol. Water Resour., 36 (2016), 10–22.
[23] Rakhimov, A. and Ahmedov, A. On the fundamental solution of the Cauchy problem for
time fractional diffusion equation on the sphere, Malays. J. Math. Sci., 6 (2) (2012), 215–226.
[24] Rashidinia, J., Molavi-Arabshahi, M. and Yousefi, M. An efficient approach for solving a
class of fractional anomalous diffusion equation with convergence, Phys. Scr., 99 (2024),
105203.
[25] Ray, S.S., Chaudhuri, K.S. and Bera, R.K. Application of modified decomposition method for
the analytical solution of space fractional diffusion equation, Appl. Math. Comput., 197(2)
(2008), 667–673.
[26] Ray, S.S. Analytical solution for the space fractional diffusion equation by two-step Adomian
Decomposition Method, Commun. Nonlinear Sci. Numer. Simul., 14(3) (2009), 1295–1306.
[27] Singh, A.K. and Mehra, M. Difference methods for stochastic space fractional diffusion
equation driven by additive space–time white noise via Wong–Zakai approximation, J. Math.
Chem., 61 (2023), 2263–2283.
[28] Sultana, S. Analysis of a generalized proportional fractional stochastic differential equa-
tion incorporating Carathéodory’s approximation and applications, Open Phys., 22 (2024),
20240155.
[29] Sylvain, T.T.A., Patrice, E.L.E.A., Marie, E.E.J. and Hubert, B.-B.G. A unified three-
dimensional extended fractional analytical solution for air pollutants dispersion, Fractals,
30 (7) (2022), 2250180.
[30] Yuan, X., Yu, Y. and Ren, G. Random attractors for fractional stochastic reaction–diffusion
systems with fractional Brownian motion, Chaos Solitons Fractals, 183 (2025), 114579.
[31] Zhang, Y., Zhou, D., Wei, W. and Chen, X. Hierarchical fractional advection‐dispersion
equation (FADE) to quantify anomalous transport in river corridor over a broad spectrum
of scales: Theory and applications, Mathematics, 9 (6) (2021), 639.
