Multidimensional problems for nonlinear fractional Schrödinger differential and difference equations
Ashyralyev A. Hicdurmaz B.
15 March 2021John Wiley and Sons Ltd
Mathematical Methods in the Applied Sciences
2021#44Issue 42731 - 2751 pp.
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.
bounded solution , existence and uniqueness , finite difference method , fractional Schrödinger differential equation
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Department of Mathematics, Near East University, Nicosia, Turkey
Department of Applied Mathematics, Peoples Friendship University Russia, Moscow, Russian Federation
Department of Mathematics, Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Department of Mathematics, Istanbul Medeniyet University, Istanbul, Turkey
Department of Mathematics
Department of Applied Mathematics
Department of Mathematics
Department of Mathematics
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