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Journal of Applied Mathematics and Computing
Published in: Journal of Applied Mathematics and Computing 5/2022

18-11-2021 | Original Research

A coupled system involving nonlinear fractional q-difference stationary Schrödinger equation

Authors: Zhongyun Qin, Shurong Sun

Published in: Journal of Applied Mathematics and Computing | Issue 5/2022

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Abstract

In this paper, we investigate the solvability for a coupled system involving nonlinear fractional q-difference stationary Schrödinger equation. The existence criterion of solutions is established by Schauder fixed point theorem, while the existence of iterative positive solutions is derived by monotone iteration method. As applications, an example is presented to illustrate the main results.
previous article Numerical framework for the Caputo time-fractional diffusion equation with fourth order derivative in space
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Literature
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Annaby, M., Mansour, Z.: Fractional \(q\)-Difference Equations. Springer, Berlin, Heidelberg (2012)CrossRef
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Asaithambi, A.: Numerical solution of the one-dimensional time-independent Schrödinger’s equation by recursive evaluation of derivatives. Appl. Math. Comput. 215, 4400–4405 (2010)
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Li, X., Han, Z., Li, X.: Boundary value problems of fractional \(q\)-difference Schrödinger equations. Appl. Math. Lett. 46, 100–105 (2015)MathSciNetCrossRef
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Wang, G.: Twin iterative positive solutions of fractional \(q\)-difference Schrödinger equations. Appl. Math. Lett. 76, 103–109 (2018)MathSciNetCrossRef
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Ferreira, R.: Positive solutions for a class of boundary value problems with fractional \(q\)-differences. Comput. Math. Appl. 61, 367–373 (2011)MathSciNetCrossRef
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Sladana, D., Predrag, M., Miomir, S.: Fractional integrals and derivatives in \(q\)-calculus. Appl. Anal. Discrete Math. 1, 311–323 (2007)MathSciNetCrossRef
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Alves, E., Ma, T., Pelicer, M.: Mauricio,Monotone positive solutions for a fourth order equation with nonlinear boundary conditions. Nonlinear Anal. Theory Methods Appl. 71, 3834–3841 (2009)CrossRef
Metadata
Title
A coupled system involving nonlinear fractional q-difference stationary Schrödinger equation
Authors
Zhongyun Qin
Shurong Sun
Publication date
18-11-2021
Publisher
Springer Berlin Heidelberg
Published in
Journal of Applied Mathematics and Computing / Issue 5/2022
Print ISSN: 1598-5865
Electronic ISSN: 1865-2085
DOI
https://doi.org/10.1007/s12190-021-01664-0

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