Институт математики и математического моделирования

“Analysis and Applied Mathematics” Еженедельный онлайн семинар 58

Date: Tuesday, April 28, 2026

Time: 14.00-15.00 (Istanbul) = 13.00-14.00 (Ghent) = 16.00-17.00 (Almaty)

Zoom link: https://us02web.zoom.us/j/6678270445?pwd=SFNmQUIvT0tRaHlDaVYrN3l5bzJVQT09 ,

Conference ID: 667 827 0445, Access code: 1

Speaker:

Assoc. Prof. Dr. Betül Hiçdurmaz

Istanbul Medeniyet University, Istanbul, Türkiye

Title: A unified abstract approach to time-fractional semilinear Schrödinger equations with trapping potentials and spatially disordered coefficients

Abstract: This study investigates a class of time-fractional semilinear Schrödinger equations within a general abstract operator framework. Unlike the majority of existing studies, the present formulation is established at the level of self-adjoint positive definite operators on Hilbert spaces for semi-linear case of time-fractional Schrödinger equations.

This setting naturally incorporates variable-coefficient and nonstandard spatial operators,thereby extending the applicability of time-fractional Schrödinger models to more general heterogeneous media.

Under standard Lipschitz conditions on the nonlinear term, existence and uniqueness of mild solutions are established using operator-theoretic techniques. A first-order time discretization scheme based on the Grünwald–Letnikov approximation is constructed and analyzed within the same abstract framework. Stability and convergence results are rigorously derived, and optimal first-order accuracy in time is proved under suitable regularity assumptions. The analysis is performed at the operator level, ensuring independence from particular spatial discretization choices.

Numerical experiments in one- and two-dimensional settings, including variable-coefficient operators and various nonlinear interaction terms, confirm the theoretical findings and demonstrate the robustness and reliability of the proposed method. The abstract framework developed in this study provides a flexible foundation for further investigations of higher-order schemes and fully discrete approximations for fractional quantum evolution problems.

Abstracts and forthcoming talks can be found on our webpage
https://sites.google.com/view/aam-seminars

Kazakh Mathematical Journal

“Analysis and Applied Mathematics” Еженедельный онлайн семинар 58

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