In this study, we propose a distributed-order fractional diffusion model that incorporates a Bessel-type fractional derivative in time and a Riesz fractional derivative in space, providing a versatile framework to describe complex diffusion processes exhibiting both memory effects and nonlocal interactions. To numerically solve the proposed model, we develop a fully discrete scheme combining the Bernstein polynomial collocation method for the temporal distributed-order derivative with a finite difference approximation for the spatial Riesz derivative. The temporal approximation ensures high-order accuracy and efficient evaluation of the distributed-order operator, while the spatial discretization captures the nonlocal behavior of the Riesz derivative. A rigorous theoretical analysis of the scheme is carried out, establishing unconditional stability and second-order convergence in both time and space. Numerical simulations validate the theoretical results, demonstrating that the method accurately captures the dynamics of the distributed-order fractional diffusion process and achieves the expected convergence rates. The proposed framework offers a powerful and reliable tool for modeling and simulating complex diffusion phenomena, and it can be further extended to multi-dimensional and variable-order settings for broader applications in physics, engineering, and applied sciences.
Mankhi Jebur Alaayedi, A., Irandoust-Pakchin, S., & Derakhshan, M. H. (2026). A Fully Discrete Bernstein Collocation Scheme for Distributed-Order Fractional Diffusion Equations with Bessel and Riesz Derivatives. Analytical and Numerical Solutions for Nonlinear Equations, (), -. doi: 10.22128/ansne.2026.3442.1238
MLA
Ali Mankhi Jebur Alaayedi; Safar Irandoust-Pakchin; Mohammad Hossein Derakhshan. "A Fully Discrete Bernstein Collocation Scheme for Distributed-Order Fractional Diffusion Equations with Bessel and Riesz Derivatives", Analytical and Numerical Solutions for Nonlinear Equations, , , 2026, -. doi: 10.22128/ansne.2026.3442.1238
HARVARD
Mankhi Jebur Alaayedi, A., Irandoust-Pakchin, S., Derakhshan, M. H. (2026). 'A Fully Discrete Bernstein Collocation Scheme for Distributed-Order Fractional Diffusion Equations with Bessel and Riesz Derivatives', Analytical and Numerical Solutions for Nonlinear Equations, (), pp. -. doi: 10.22128/ansne.2026.3442.1238
VANCOUVER
Mankhi Jebur Alaayedi, A., Irandoust-Pakchin, S., Derakhshan, M. H. A Fully Discrete Bernstein Collocation Scheme for Distributed-Order Fractional Diffusion Equations with Bessel and Riesz Derivatives. Analytical and Numerical Solutions for Nonlinear Equations, 2026; (): -. doi: 10.22128/ansne.2026.3442.1238
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