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Multidimensional problems for nonlinear fractional Schrödinger differential and difference equations
Author(s) -
Ashyralyev Allaberen,
Hicdurmaz Betul
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5866
Subject(s) - mathematics , uniqueness , hilbert space , bounded function , nonlinear system , boundary value problem , operator (biology) , dirichlet boundary condition , mathematical analysis , space (punctuation) , biochemistry , chemistry , physics , linguistics , philosophy , repressor , quantum mechanics , transcription factor , gene
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.