3 citations · 5 across the 5 of their papers we have counts for
6 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…
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 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…
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…