Boundary value problems for the diffusion equation of the variable order in differential and difference settings. - Anatoly A. Alikhanov (Appl. Math. Comput., 2012)

Numerical methods of solutions of boundary value problems for the multi-term variable-distributed order diffusion equation. - Anatoly A. Alikhanov (Appl. Math. Comput., 2015)

A new difference scheme for the time fractional diffusion equation. - Anatoly A. Alikhanov (J. Comput. Phys., 2015)

A Higher Order Difference Scheme for the Time Fractional Diffusion Equation with the Steklov Nonlocal Boundary Value Problem of the Second Kind. - Anatoly A. Alikhanov; Inna Z. Kodzokova (NAA, 2016)

A Difference Method for Solving the Steklov Nonlocal Boundary Value Problem of Second Kind for the Time-Fractional Diffusion Equation. - Anatoly A. Alikhanov (Comput. Methods Appl. Math., 2017)

A Time-Fractional Diffusion Equation with Generalized Memory Kernel in Differential and Difference Settings with Smooth Solutions. - Anatoly A. Alikhanov (Comput. Methods Appl. Math., 2017)

The Temporal Second Order Difference Schemes Based on the Interpolation Approximation for Solving the Time Multi-term and Distributed-Order Fractional Sub-diffusion Equations. - Guang-hua Gao; Anatoly A. Alikhanov; Zhi-Zhong Sun (J. Sci. Comput., 2017)

Fast Iterative Method with a Second-Order Implicit Difference Scheme for Time-Space Fractional Convection-Diffusion Equation. - Xian-Ming Gu; Ting-Zhu Huang; Cui-Cui Ji; Bruno Carpentieri; Anatoly A. Alikhanov (J. Sci. Comput., 2017)

Temporal second order difference schemes for the multi-dimensional variable-order time fractional sub-diffusion equations. - Ruilian Du; Anatoly A. Alikhanov; Zhi-Zhong Sun (Comput. Math. Appl., 2020)

A high-order L2 type difference scheme for the time-fractional diffusion equation. - Anatoly A. Alikhanov; Chengming Huang (Appl. Math. Comput., 2021)

Numerical analysis of multi-term time-fractional nonlinear subdiffusion equations with time delay: What could possibly go wrong? - Mahmoud A. Zaky; Ahmed S. Hendy; Anatoly A. Alikhanov; Vladimir G. Pimenov (Commun. Nonlinear Sci. Numer. Simul., 2021)

A second order difference scheme for time fractional diffusion equation with generalized memory kernel. - Aslanbek Khibiev; Anatoly A. Alikhanov; Chengming Huang (CoRR, 2021)

Partially Explicit Time Discretization for Time Fractional Diffusion Equation. - Jiuhua Hu; Anatoly A. Alikhanov; Yalchin Efendiev; Wing Tat Leung (CoRR, 2021)

Data-Driven Discovery of Time Fractional Differential Equations. - Abhishek Kumar Singh; Mani Mehra; Anatoly A. Alikhanov (ICCS (1), 2022)

Partially explicit time discretization for nonlinear time fractional diffusion equations. - Wenyuan Li 004; Anatoly A. Alikhanov; Yalchin Efendiev; Wing Tat Leung (Commun. Nonlinear Sci. Numer. Simul., 2022)

A class of time-fractional diffusion equations with generalized fractional derivatives. - Anatoly A. Alikhanov; Chengming Huang (J. Comput. Appl. Math., 2022)

Stability analysis of a second-order difference scheme for the time-fractional mixed sub-diffusion and diffusion-wave equation. - Anatoly A. Alikhanov; Mohammad Shahbazi Asl; Chengming Huang (CoRR, 2023)

A computational macroscale model for the time fractional poroelasticity problem in fractured and heterogeneous media. - Aleksei Tyrylgin; Maria V. Vasilyeva; Anatoly A. Alikhanov; Dongwoo Sheen (J. Comput. Appl. Math., 2023)

A High-Order Discrete Energy Decay and Maximum-Principle Preserving Scheme for Time Fractional Allen-Cahn Equation. - Guoyu Zhang; Chengming Huang; Anatoly A. Alikhanov; Baoli Yin (J. Sci. Comput., 2023)

Modified least squares method and a review of its applications in machine learning and fractional differential/integral equations. - Abhishek Kumar Singh; Mani Mehra; Anatoly A. Alikhanov (CoRR, 2024)

Robust finite difference scheme for the non-linear generalized time-fractional diffusion equation with non-smooth solution. - Nikki Kedia; Anatoly A. Alikhanov; Vineet Kumar Singh (Math. Comput. Simul., 2024)

A Second-Order Difference Scheme for Generalized Time-Fractional Diffusion Equation with Smooth Solutions. - Aslanbek Khibiev; Anatoly A. Alikhanov; Chengming Huang (Comput. Methods Appl. Math., 2024)

A second-order difference scheme for the nonlinear time-fractional diffusion-wave equation with generalized memory kernel in the presence of time delay. - Anatoly A. Alikhanov; Mohammad Shahbazi Asl; Chengming Huang; Aslanbek Khibiev (J. Comput. Appl. Math., 2024)

Multiscale model reduction for the time fractional thermoporoelasticity problem in fractured and heterogeneous media. - Anatoly A. Alikhanov; Huiran Bai; Jian Huang; Aleksei Tyrylgin; Yin Yang (J. Comput. Appl. Math., 2025)

Numerical method for fractional sub-diffusion equation with space-time varying diffusivity and smooth solution. - Xuhao Li; Patricia J. Y. Wong; Anatoly A. Alikhanov (J. Comput. Appl. Math., 2025)

A high-order compact difference scheme for the multi-term time-fractional Sobolev-type convection-diffusion equation. - Anatoly A. Alikhanov; Poonam Yadav; Vineet Kumar Singh; Mohammad Shahbazi Asl (Comput. Appl. Math., 2025)