×

Existence of positive solutions for a discrete fractional boundary value problem. (English) Zbl 1343.39017

Summary: This paper is concerned with the existence of positive solutions to a discrete fractional boundary value problem. By using the Krasnosel’skii and Schaefer fixed point theorems, the existence results are established. Additionally, examples are provided to illustrate the effectiveness of the main results.

MSC:

39A12 Discrete version of topics in analysis
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Samko SG, Kilbas AA, Marichev OI: Fractional Integrals and Derivatives. Theory and Applications. Gordon & Breach, Yverdon; 1993. · Zbl 0818.26003
[2] Podlubny, I., Mathematics in Science and Engineering 198 (1999), New York
[3] Bai ZB, Lü HS: Positive solutions for boundary value problem of nonlinear fractional differential equation.J. Math. Anal. Appl. 2005, 311:495-505. · Zbl 1079.34048 · doi:10.1016/j.jmaa.2005.02.052
[4] Zhang, SQ, Positive solutions for boundary value problems of nonlinear fractional differential equations, No. 2006 (2006)
[5] Jafari H, Gejji VD: Positive solutions of nonlinear fractional boundary value problems using Adomian decomposition method.Appl. Math. Comput. 2006, 180:700-706. · Zbl 1102.65136 · doi:10.1016/j.amc.2006.01.007
[6] Dehghani R, Ghanbari K: Triple positive solutions for boundary value problem of a nonlinear fractional differential equation.Bull. Iran. Math. Soc. 2007,33(2):1-14. · Zbl 1148.34008
[7] Wang JH, Xiang HJ, Liu ZG: Positive solutions for three-point boundary value problems of nonlinear fractional differential equations withP-Laplacian.Far East J. Appl. Math. 2009,37(1):33-47. · Zbl 1181.26019
[8] Wang, JH; Xiang, HJ; Liu, ZG, Upper and lower solutions method for a class of singular fractional boundary value problems with P-Laplacian, No. 2010 (2010)
[9] Cai, G., Positive solutions for boundary value problems of fractional differential equations with P-Laplacian operator, No. 2012 (2012)
[10] Atici FM, Eloe PW: Two-point boundary value problems for finite fractional difference equations.J. Differ. Equ. Appl. 2011, 17:445-456. · Zbl 1215.39002 · doi:10.1080/10236190903029241
[11] Goodrich CS: On a first-order semipositone discrete fractional boundary value problem.Arch. Math. 2012, 99:509-518. · Zbl 1263.26016 · doi:10.1007/s00013-012-0463-2
[12] Lv, WD, Existence of solutions for discrete fractional boundary value problems with a P-Laplacian operator, No. 2012 (2012)
[13] Goodrich CS: Existence of a positive solution to a system of discrete fractional boundary value problems.Appl. Math. Comput. 2011, 217:4740-4753. · Zbl 1215.39003 · doi:10.1016/j.amc.2010.11.029
[14] Atici FM, Eloe PW: A transform method in discrete fractional calculus.Int. J. Differ. Equ. 2007,2(2):165-176.
[15] Goodrich CS: On discrete sequential fractional boundary value problems.J. Math. Anal. Appl. 2012, 385:111-124. · Zbl 1236.39008 · doi:10.1016/j.jmaa.2011.06.022
[16] Goodrich CS: Positive solutions to boundary value problems with nonlinear boundary conditions.Nonlinear Anal. 2012, 75:417-432. · Zbl 1237.34153 · doi:10.1016/j.na.2011.08.044
[17] Goodrich CS: On discrete fractional three-point boundary value problems.J. Differ. Equ. Appl. 2012, 18:397-415. · Zbl 1253.26010 · doi:10.1080/10236198.2010.503240
[18] Goodrich CS: Nonlocal systems of BVPs with asymptotically superlinear boundary conditions.Comment. Math. Univ. Carol. 2012, 53:79-97. · Zbl 1249.34054
[19] Atici FM, Sengul S: Modeling with fractional difference equations.J. Math. Anal. Appl. 2010, 369:1-9. · Zbl 1204.39004 · doi:10.1016/j.jmaa.2010.02.009
[20] Zeidler E: Nonlinear Functional Analysis and Applications, I: Fixed Point Theorems. Springer, New York; 1986. · Zbl 0583.47050 · doi:10.1007/978-1-4612-4838-5
[21] Atici FM, Eloe PW: Initial value problems in discrete fractional calculus.Proc. Am. Math. Soc. 2009, 137:981-989. · Zbl 1166.39005 · doi:10.1090/S0002-9939-08-09626-3
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.