Multidimensional problems for nonlinear fractional Schrödinger differential and difference equations

In the present paper, a nonlinear fractional Schrödinger integro-differential equation is considered in a Hilbert space. Operator approach is applied on multidimensional problems with nonlinearity that deserve a studious treatment. In this paper, theorems on existence and uniqueness of a bounded solution for the abstract problem are achieved. Additionally, existence theorems are obtained for first and second orders of accuracy difference schemes of the abstract problem. Furthermore, theorems are applied on a one-dimensional problem with nonlocal condition and a multidimensional problem with Dirichlet boundary condition. Numerical results and illustrations are presented to show the effectiveness of the theoretical results. © 2019 John Wiley & Sons, Ltd.

Авторы
Ashyralyev A. 1, 2, 3 , Hicdurmaz B.4
Издательство
John Wiley and Sons Ltd
Язык
Английский
Статус
Опубликовано
Год
2019
Организации
  • 1 Department of Mathematics, Near East University, Nicosia, Turkey
  • 2 Department of Applied Mathematics, Peoples' Friendship University of Russia (RUDN University), Ul Miklukho Maklaya 6, Moscow, 117198, Russian Federation
  • 3 Department of Mathematics, Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
  • 4 Department of Mathematics, Istanbul Medeniyet University, Istanbul, Turkey
Ключевые слова
bounded solution; existence and uniqueness; finite difference method; fractional Schrödinger differential equation
Дата создания
24.12.2019
Дата изменения
24.12.2019
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/55476/
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