904 citations · 1.4k across the 17 of their papers we have counts for
17 papers
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
The least squares method provides the best-fit curve by minimizing the total squares error. In this work, we provide the modified least squares method based on the fractional ortho…
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
This study investigates a class of initial-boundary value problems pertaining to the time-fractional mixed sub-diffusion and diffusion-wave equation (SDDWE). To facilitate the deve…
A high-order discrete energy decay and maximum-principle preserving scheme for time fractional Allen-Cahn equation
Guoyu Zhang, Chengming Huang, Anatoly A. Alikhanov +1
The shifted fractional trapezoidal rule (SFTR) with a special shift is adopted to construct a finite difference scheme for the time-fractional Allen-Cahn (tFAC) equation. Some esse…
A computational macroscale model for the time fractional poroelasticity problem in fractured and heterogeneous media
Aleksei Tyrylgin, Maria Vasilyeva, Anatoly Alikhanov +1
In this work, we introduce a time memory formalism in poroelasticity model that couples the pressure and displacement. We assume this multiphysics process occurs in multicontinuum…
Partially Explicit Time Discretization for Nonlinear Time Fractional Diffusion Equations
Wenyuan Li, Anatoly Alikhanov, Yalchin Efendiev +1
Nonlinear time fractional partial differential equations are widely used in modeling and simulations. In many applications, there are high contrast changes in media properties. For…
Partially Explicit Time Discretization for Time Fractional Diffusion Equation
Jiuhua Hu, Anatoly Alikhanov, Yalchin Efendiev +1
Time fractional PDEs have been used in many applications for modeling and simulations. Many of these applications are multiscale and contain high contrast variations in the media p…
A second order difference scheme for time fractional diffusion equation with generalized memory kernel
Aslanbek Khibiev, Anatoly Alikhanov, Chengming Huang
In the current work we build a difference analog of the Caputo fractional derivative with generalized memory kernel (L2-1 formula). The fundamental features of this differe…
A high-order L2 type difference scheme for the time-fractional diffusion equation
Anatoly A. Alikhanov, Chengming Huang
The present paper is devoted to constructing L2 type difference analog of the Caputo fractional derivative. The fundamental features of this difference operator are studied and it…
The Crank-Nicholson type compact difference scheme for a loaded time-fractional Hallaire's equation
Anatoly Alikhanov, Murat Beshtokov, Mani Mehra
In this paper, we study loaded modified diffusion equation (the Hallaire equation with the fractional derivative with respect to time). The compact finite difference scheme of Cran…
About one method of parallelization of calculations during the reconstruction of a tomographic image
A. A. Alikhanov, A. M. Apekov, Z. A. Kokov +2
A new method for solving systems of linear algebraic equations of a special type arising in solving problems of image reconstruction has been proposed. This method, due to a certai…
Fast iterative method with a second order implicit difference scheme for time-space fractional convection-diffusion equations
Xian-Ming Gu, Ting-Zhu Huang, Cui-Cui Ji +2
In this paper we want to propose practical numerical methods to solve a class of initial-boundary problem of time-space fractional convection-diffusion equations (TSFCDEs). To star…
A difference method of solving the Steklov nonlocal boundary value problem of the second kind for the time-fractional diffusion equation
A. A. Alikhanov
We consider difference schemes for the time-fractional diffusion equation with variable coefficients and nonlocal boundary conditions containing real parameters , and . B…
A new difference scheme for the time fractional diffusion equation
A. A. Alikhanov
In this paper we construct a new difference analog of the Caputo fractional derivative (called the - formula). The basic properties of this difference operator are investi…
Stability and convergence of difference schemes approximating a two-parameter nonlocal boundary value problem for time-fractional diffusion equation
A. A. Alikhanov
Difference schemes for the time-fractional diffusion equation with variable coefficients and nonlocal boundary conditions containing real parameters and are considered. By…
Numerical methods of solutions of boundary value problems for the multi-term variable-distributed order diffusion equation
A. A. Alikhanov
Solutions of the Dirichlet and Robin boundary value problems for the multi-term variable-distributed order diffusion equation are studied. A priori estimates for the corresponding…
A Priori Estimates for Solutions of Boundary Value Problems for Fractional-Order Equations
A. A. Alikhanov
We consider boundary value problems of the first and third kind for the diffusionwave equation. By using the method of energy inequalities, we find a priori estimates for the solut…
Boundary value problems for the diffusion equation of the variable order in differential and difference settings
A. A. Alikhanov
Solutions of boundary value problems for a diffusion equation of fractional and variable order in differential and difference settings are studied. It is shown that the method of e…