Geodesic
Fractional differential equations with integral boundary conditions
Wang, Xuhuan1 ; Wang, Liping2 ; Zeng, Qinghong3
1 Department of Education Science, Pingxiang University, Pingxiang, Jiangxi 337055, China
2 Department of Education Science, Pingxiang University, Pingxiang, Jiangxi 337055, China
3 Department of Mathematics, Baoshan University, Baoshan, Yunnan 678000, China
Journal of nonlinear sciences and its applications, Tome 8 (2015) no. 4, p. 309-314.

Voir la notice de l'article provenant de la source International Scientific Research Publications

In this paper, the existence of solutions of fractional differential equations with integral boundary conditions is investigated. The upper and lower solutions combined with monotone iterative technique is applied. Problems of existence and unique solutions are discussed.
DOI : 10.22436/jnsa.008.04.03
Classification : 34B37, 34B15
Keywords: Fractional differential equations, upper and lower solutions, monotone iterative, convergence, integral boundary conditions.

Wang, Xuhuan 1 ; Wang, Liping 2 ; Zeng, Qinghong 3

1 Department of Education Science, Pingxiang University, Pingxiang, Jiangxi 337055, China
2 Department of Education Science, Pingxiang University, Pingxiang, Jiangxi 337055, China
3 Department of Mathematics, Baoshan University, Baoshan, Yunnan 678000, China 
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Wang, Xuhuan; Wang, Liping; Zeng, Qinghong. Fractional differential equations with integral boundary conditions. Journal of nonlinear sciences and its applications, Tome 8 (2015) no. 4, p. 309-314. doi : 10.22436/jnsa.008.04.03. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.008.04.03/

[1] Agarwal, R. P.; Arshad, S.; O'Regan, D.; Lupulescu, V. Fuzzy fractional integral equations under compactness type condition , Fract. Calc. Appl. Anal., Volume 15 (2012), pp. 572-590

[2] Al-Refai, M.; M. A. Hajji Monotone iterative sequences for nonlinear boundary value problems of fractional order, Nonlinear Anal., Volume 74 (2011), pp. 3531-3539

[3] Arshad, S.; Lupulescu, V.; O'Regan, D. \(L^P\) -solutions for fractional integral equations, Fract. Calc. Appl. Anal., Volume 17 (2014), pp. 259-276

[4] T. Jankowski Differential equations with integral boundary conditions, J. Comput. Appl. Math., Volume 147 (2002), pp. 1-8

[5] Jankowski, T. Fractional equations of Volterra type involving a Riemann-Liouville derivative, Appl. Math. Letter, Volume 26 (2013), pp. 344-350

[6] Jankowski, T. Boundary problems for fractional differential equations , Appl. Math. Letter, Volume 28 (2014), pp. 14-19

[7] Kilbas, A. A.; Srivastava, H. M.; J. J. Trujillo Theory and Applications of Fractional Differential Equations, in: North-Holland Mathematics Studies, vol. 204, Elsevier, Amsterdam, 2006

[8] Lakshmikantham, V.; Vatsala, A. S. Theory of fractional differential inequalities and applications, Commun. Appl. Anal., Volume 11 (2007), pp. 395-402

[9] Lakshmikanthan, V.; Vatsala, A. S. General uniqueness and monotone iterative technique for fractional differential equations, Appl. Math. Letter, Volume 21 (2008), pp. 828-834

[10] Li, N.; Wang, C. Y. New existence results of positive solution for a class of nonlinear fractional differential equations, Acta. Math. Scientia, Volume 33 (2013), pp. 847-854

[11] Liang, J. T.; Liu, Z. H.; Wang, X. H. Solvability for a Couple System of Nonlinear Fractional Differential Equations in a Banach Space, Fract. Calc. Appl. Anal., Volume 16 (2013), pp. 51-63

[12] Lin, L.; Liu, X.; Fang, H. Method of upper and lower solutions for fractional differential equations, Electron. J. Differential Equations, Volume 100 (2012), pp. 1-13

[13] McRae, F. A. Monotone iterative technique and existence results for fractional differential equations , Nonlinear Anal., Volume 71 (2009), pp. 6093-6096

[14] Nanware, A.; Dhaigude, D. B. Existence and uniqueness of solutions of differential equations of fractional order with integral boundary conditions, J. Nonlinear Sci. Appl., Volume 7 (2014), pp. 246-254

[15] I. Podlubny Fractional Differential Equations, Mathematics in Science and Engineering, Academic Press, New York, 1999

[16] Shi, A.; S. Zhang Upper and lower solutions method and a fractional differential equation boundary value problem, Electron. J. Qual. Theory Differ. Equ., Volume 30 (2009), pp. 1-13

[17] Wang, G. Monotone iterative technique for boundary value problems of a nonlinear fractional differential equations with deviating arguments , J. Comput. Appl. Math., Volume 236 (2012), pp. 2425-2430

[18] Wang, T.; Xie, F. Existence and uniqueness of fractional differential equations with integral boundary conditions, J. Nonlinear Sci. Appl., Volume 2 (2009), pp. 206-212

[19] X. H. Wang Impulsive boundary value problem for nonlinear differential equations of fractional order, Comput. Math. Appl., Volume 62 (2011), pp. 2383-2391

[20] Z. J. Yao New results of positive solutions for second-order nonlinear three-point integral boundary value problems , J. Nonlinear Sci. Appl., Volume 8 (2015), pp. 93-98

[21] Zhang, S. Monotone iterative method for initial value problem involving Riemann-Liouville fractional derivatives, Nonlinear Anal., Volume 71 (2009), pp. 2087-2093

[22] Zhang, S. Q.; X. W. Su The existence of a solution for a fractional differential equation with nonlinear boundary conditions considered using upper and lower solutions inreverse order, Comput. Math. Appl., Volume 62 (2011), pp. 1269-1274

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