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Journal of Applied Mathematics and Computing
Published in: Journal of Applied Mathematics and Computing 1-2/2016

01-02-2016 | Original Research

Anti-periodic boundary value problems for fractional \(q\)-difference equations

Authors: Xinhui Li, Zhenlai Han, Shurong Sun

Published in: Journal of Applied Mathematics and Computing | Issue 1-2/2016

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Abstract

In this paper, we study the boundary value problem with anti-periodic boundary conditions involving the Caputo fractional \(q\)-derivative. By means of the Banach contraction mapping principle and Scheafer fixed point theorem, some results of the existence and uniqueness of solutions are obtained. At last, examples are presented to illustrate our main results.
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Literature
1.
Agarwal, R.: Certain fractional \(q\)-integrals and \(q\)-derivatives. Proc. Camb. Philos. Soc. 66, 365–370 (1969)CrossRefMATH
2.
Rajković, P., Marinković, S., Stanković, M.: Fractional integrals and derivatives in \(q\)-calculus. Appl. Anal. Discret. Math. 1(1), 311–323 (2007)CrossRefMATH
3.
Annaby, M., Mansour, Z.: \(q\)-Fractional Calculus and Equations. Springer-Verlag, Berlin Heidelberg (2012)
4.
5.
Field, C., Joshi, N., Nijhoff, F.: \(q\)-difference equations of KdV type and Chazy-type second-degree difference equations. Phys. A Math. Theor. 41(33), 1–13 (2008)MathSciNet
6.
7.
Abreu, L.: Sampling theory associated with \(q\)-difference equations of the Sturm-Liouville type. J. Phys. A. 38(48), 10311–10319 (2005)MathSciNetCrossRefMATH
8.
Ernst, T.: A Comprehensive Treatment of \(q\)-Calculus. Springer, Basel (2012)CrossRef
9.
Cheng, H.: Canonical quantization of Yang-Mills theories. Perspectives in Mathematical Physics. International Press, Somerville (1994)
10.
11.
Cabada, A., Hamdi, Z.: Nonlinear fractional differential equations with integral boundary value conditions. Appl. Math. Comput. 228, 251–257 (2014)MathSciNetCrossRef
12.
Lv, Z.: Existence results for \(m\)-point boundary value problems of nonlinear fractional differential equations with \(p\)-Laplacian operator. Adv. Differ. Equ. 2014(69), 1–16 (2014)
13.
Ferreira, R.: Nontrivial solutions for fractional \(q\)-difference boundary value problems. Electron. J. Qual. Theory Differ. Equ. 70, 1–10 (2010)CrossRef
14.
Li, X., Han, Z., Sun, S.: Existence of positive solutions of nonlinear fractional \(q\)-difference equation with parameter. Adv. Differ. Equ. 2013(260), 1–13 (2013)MathSciNet
15.
Zhou, W., Liu, H.: Existence solutions for boundary value problem of nonlinear fractional \(q\)-difference equations. Adv. Differ. Equ. 1(113), 1–12 (2013)CrossRefMATH
16.
Yang, W.: Anti-periodic bounndary value problems involving nonlinear fractional \(q-\)difference equations. Malaya J. Mat. 4(1), 107–114 (2013)
17.
18.
Wang, F., Liu, Z.: Anti-periodic fractional boundary value problems for nonlinear differential equations of fractional order. Adv. Differ. Equ. 2012(116), 1–12 (2012)MATH
19.
Benchohra, M., Hamidi, N., Henderson, J.: Fractional differential equations with anti-periodic boundary conditions. Numer. Funct. Anal. Optim. 34(4), 404–414 (2013)MathSciNetCrossRefMATH
20.
Smart, D.: Fixed Point Theorems. Cambridge University Press, Cambridge (1980)MATH
Metadata
Title
Anti-periodic boundary value problems for fractional -difference equations
Authors
Xinhui Li
Zhenlai Han
Shurong Sun
Publication date
01-02-2016
Publisher
Springer Berlin Heidelberg
Published in
Journal of Applied Mathematics and Computing / Issue 1-2/2016
Print ISSN: 1598-5865
Electronic ISSN: 1865-2085
DOI
https://doi.org/10.1007/s12190-015-0868-8

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