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A coupled system of nonlinear fractional differential equations with multipoint fractional boundary conditions on an unbounded domain. (English) Zbl 1242.34010
Summary: This paper investigates the existence of solutions for a coupled system of nonlinear fractional differential equations with $m$-point fractional boundary conditions on an unbounded domain. Some standard fixed point theorems are applied to obtain the main results. The paper concludes with two illustrative examples.

MSC:
34A08Fractional differential equations
WorldCat.org
Full Text: DOI
References:
[1] M. P. Lazarević and A. M. Spasić, “Finite-time stability analysis of fractional order time-delay systems: Gronwall’s approach,” Mathematical and Computer Modelling, vol. 49, no. 3-4, pp. 475-481, 2009. · Zbl 1165.34408 · doi:10.1016/j.mcm.2008.09.011
[2] I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999. · Zbl 0924.34008
[3] D. Baleanu, K. Diethelm, E. Scalas, and J. J. Trujillo, Fractional Calculus Models and Numerical Methods (Series on Complexity, Nonlinearity and Chaos), World Scientific, 2012. · Zbl 1248.26011
[4] R. L. Magin, Fractional Calculus in Bioengineering, Begell House, Connecticut, Conn, USA, 2006.
[5] A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204 of North-Holland Mathematics Studies, Elsevier Science, Amsterdam, The Netherlands, 2006. · Zbl 1092.45003
[6] J. Sabatier, O. P. Agrawal, and J. A. T. Machado, Eds., Advances in Fractional Calculus, Springer, Dordrecht, The Netherlands, 2007. · Zbl 1116.00014 · doi:10.1007/978-1-4020-6042-7
[7] S. Liang and J. Zhang, “Positive solutions for boundary value problems of nonlinear fractional differential equation,” Nonlinear Analysis, vol. 71, no. 11, pp. 5545-5550, 2009. · Zbl 1185.26011 · doi:10.1016/j.na.2009.04.045 · eudml:231936
[8] S. Zhang, “Existence results of positive solutions to boundary value problem for fractional differential equation,” Positivity, vol. 13, no. 3, pp. 583-599, 2009. · Zbl 1202.26018 · doi:10.1007/s11117-008-2260-5
[9] B. Ahmad and J. J. Nieto, “Existence of solutions for nonlocal boundary value problems of higher-order nonlinear fractional differential equations,” Abstract and Applied Analysis, vol. 2009, Article ID 494720, 9 pages, 2009. · Zbl 1186.34009 · doi:10.1155/2009/494720 · eudml:45648
[10] J. Caballero Mena, J. Harjani, and K. Sadarangani, “Existence and uniqueness of positive and nondecreasing solutions for a class of singular fractional boundary value problems,” Boundary Value Problems, vol. 2009, Article ID 421310, 10 pages, 2009. · Zbl 1182.34005 · doi:10.1155/2009/421310 · eudml:45610
[11] S. Zhang, “Positive solutions to singular boundary value problem for nonlinear fractional differential equation,” Computers & Mathematics with Applications, vol. 59, no. 3, pp. 1300-1309, 2010. · Zbl 1189.34050 · doi:10.1016/j.camwa.2009.06.034
[12] B. Ahmad, “Existence of solutions for irregular boundary value problems of nonlinear fractional differential equations,” Applied Mathematics Letters, vol. 23, no. 4, pp. 390-394, 2010. · Zbl 1198.34007 · doi:10.1016/j.aml.2009.11.004
[13] Z. Bai, “On positive solutions of a nonlocal fractional boundary value problem,” Nonlinear Analysis, vol. 72, no. 2, pp. 916-924, 2010. · Zbl 1187.34026 · doi:10.1016/j.na.2009.07.033
[14] D. B\ualeanu, O. G. Mustafa, and R. P. Agarwal, “An existence result for a superlinear fractional differential equation,” Applied Mathematics Letters, vol. 23, no. 9, pp. 1129-1132, 2010. · Zbl 1200.34004 · doi:10.1016/j.aml.2010.04.049
[15] S. Bhalekar, V. Daftardar-Gejji, D. Baleanu, and R. Magin, “Fractional Bloch equation with delay,” Computers & Mathematics with Applications, vol. 61, no. 5, pp. 1355-1365, 2011. · Zbl 1217.34123 · doi:10.1016/j.camwa.2010.12.079
[16] B. Ahmad and J. J. Nieto, “Anti-periodic fractional boundary value problems,” Computers & Mathematics with Applications, vol. 62, no. 3, pp. 1150-1156, 2011. · Zbl 1228.34009 · doi:10.1016/j.camwa.2011.03.001
[17] B. Ahmad and S. K. Ntouyas, “A four-point nonlocal integral boundary value problem for fractional differential equations of arbitrary order,” Electronic Journal of Qualitative Theory of Differential Equations, no. 22, pp. 1-15, 2011. · Zbl 06528026
[18] A. Cabada and G. Wang, “Positive solutions of nonlinear fractional differential equations with integral boundary value conditions,” Journal of Mathematical Analysis and Applications, vol. 389, no. 1, pp. 403-411, 2012. · Zbl 1232.34010 · doi:10.1016/j.jmaa.2011.11.065
[19] B. Ahmad and R. P. Agarwal, “On nonlocal fractional boundary value problems,” Dynamics of Continuous, Discrete & Impulsive Systems. Series A, vol. 18, no. 4, pp. 535-544, 2011. · Zbl 1230.26003 · http://online.watsci.org/abstract_pdf/2011v18/v18n4a-pdf/9.pdf
[20] J. D. Ramírez and A. S. Vatsala, “Monotone method for nonlinear Caputo fractional boundary value problems,” Dynamic Systems and Applications, vol. 20, no. 1, pp. 73-88, 2011. · Zbl 1234.26019
[21] Y. Zhao, S. Sun, Z. Han, and M. Zhang, “Positive solutions for boundary value problems of nonlinear fractional differential equations,” Applied Mathematics and Computation, vol. 217, no. 16, pp. 6950-6958, 2011. · Zbl 1227.34011 · doi:10.1016/j.amc.2011.01.103 · eudml:231936
[22] G. Wang, S. K. Ntouyas, and L. Zhang, “Positive solutions of the three-point boundary value problem for fractional-order differential equations with an advanced argument,” Advances in Difference Equations, vol. 2011, article 2, 2011. · Zbl 1268.34158
[23] B. Ahmad and J. J. Nieto, “Riemann-Liouville fractional integro-differential equations with fractional nonlocal integral boundary conditions,” Boundary Value Problems, vol. 2011, article 36, 2011. · Zbl 1275.45004
[24] B. Ahmad, J. J. Nieto, A. Alsaedi, and M. El-Shahed, “A study of nonlinear Langevin equation involving two fractional orders in different intervals,” Nonlinear Analysis, vol. 13, no. 2, pp. 599-606, 2012. · Zbl 1238.34008 · doi:10.1016/j.nonrwa.2011.07.052
[25] B. Ahmad, “On nonlocal boundary value problems for nonlinear integro-differential equations of arbitrary fractional order,” Results in Mathematics. In press. · Zbl 1207.45014 · doi:10.1016/j.amc.2010.05.080
[26] E. Hernández, D. O’Regan, and K. Balachandran, “On recent developments in the theory of abstract differential equations with fractional derivatives,” Nonlinear Analysis, vol. 73, no. 10, pp. 3462-3471, 2010. · Zbl 1229.34004 · doi:10.1016/j.na.2010.07.035
[27] G. Wang, “Monotone iterative technique for boundary value problems of nonlinear fractional differential equation with deviating arguments,” Journal of Computational and Applied Mathematics, vol. 236, pp. 2425-2430, 2012. · Zbl 1238.65077
[28] G. Wang, R. P. Agarwal, and A. Cabada, “Existence results and monotone iterative technique for systems of nonlinear fractional differential equations,” Applied Mathematics Letters, vol. 25, pp. 1019-1024, 2012. · Zbl 1244.34008
[29] C.-Z. Bai and J.-X. Fang, “The existence of a positive solution for a singular coupled system of nonlinear fractional differential equations,” Applied Mathematics and Computation, vol. 150, no. 3, pp. 611-621, 2004. · Zbl 1061.34001 · doi:10.1016/S0096-3003(03)00294-7
[30] V. Daftardar-Gejji, “Positive solutions of a system of non-autonomous fractional differential equations,” Journal of Mathematical Analysis and Applications, vol. 302, no. 1, pp. 56-64, 2005. · Zbl 1064.34004 · doi:10.1016/j.jmaa.2004.08.007
[31] X. Su, “Boundary value problem for a coupled system of nonlinear fractional differential equations,” Applied Mathematics Letters, vol. 22, no. 1, pp. 64-69, 2009. · Zbl 1163.34321 · doi:10.1016/j.aml.2008.03.001
[32] B. Ahmad and J. J. Nieto, “Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions,” Computers & Mathematics with Applications, vol. 58, no. 9, pp. 1838-1843, 2009. · Zbl 1205.34003 · doi:10.1016/j.camwa.2009.07.091
[33] J. Wang, H. Xiang, and Z. Liu, “Positive solution to nonzero boundary values problem for a coupled system of nonlinear fractional differential equations,” International Journal of Differential Equations, vol. 2010, Article ID 186928, 12 pages, 2010. · Zbl 1207.34012 · doi:10.1155/2010/186928 · eudml:228163
[34] A. Babakhani, “Positive solutions for system of nonlinear fractional differential equations in two dimensions with delay,” Abstract and Applied Analysis, vol. 2010, Article ID 536317, 16 pages, 2010. · Zbl 1197.34155 · doi:10.1155/2010/536317 · eudml:233184
[35] V. Gafiychuk, B. Datsko, and V. Meleshko, “Mathematical modeling of time fractional reaction-diffusion systems,” Journal of Computational and Applied Mathematics, vol. 220, no. 1-2, pp. 215-225, 2008. · Zbl 1199.35152 · doi:10.1016/j.cam.2007.08.011
[36] A. Arara, M. Benchohra, N. Hamidi, and J. J. Nieto, “Fractional order differential equations on an unbounded domain,” Nonlinear Analysis, vol. 72, no. 2, pp. 580-586, 2010. · Zbl 1179.26015 · doi:10.1016/j.na.2009.06.106
[37] X. Zhao and W. Ge, “Unbounded solutions for a fractional boundary value problems on the infinite interval,” Acta Applicandae Mathematicae, vol. 109, no. 2, pp. 495-505, 2010. · Zbl 1193.34008 · doi:10.1007/s10440-008-9329-9
[38] S. Liang and J. Zhang, “Existence of three positive solutions of m-point boundary value problems for some nonlinear fractional differential equations on an infinite interval,” Computers & Mathematics with Applications, vol. 61, no. 11, pp. 3343-3354, 2011. · Zbl 1235.34079 · doi:10.1016/j.camwa.2011.04.018
[39] X. Su, “Solutions to boundary value problem of fractional order on unbounded domains in a Banach space,” Nonlinear Analysis, vol. 74, no. 8, pp. 2844-2852, 2011. · Zbl 1250.34007 · doi:10.1016/j.na.2011.01.006
[40] R. P. Agarwal, M. Benchohra, S. Hamani, and S. Pinelas, “Boundary value problems for differential equations involving Riemann-Liouville fractional derivative on the half-line,” Dynamics of Continuous, Discrete & Impulsive Systems. Series A, vol. 18, no. 2, pp. 235-244, 2011. · Zbl 1208.26012 · http://dcdis001.watam.org/volumes/abstract_pdf/2011v18/v18n2a-pdf/7.pdf
[41] S. Liang and J. Zhang, “Existence of multiple positive solutions for m-point fractional boundary value problems on an infinite interval,” Mathematical and Computer Modelling, vol. 54, no. 5-6, pp. 1334-1346, 2011. · Zbl 1235.34023 · doi:10.1016/j.mcm.2011.04.004
[42] F. Chen and Y. Zhou, “Attractivity of fractional functional differential equations,” Computers & Mathematics with Applications, vol. 62, no. 3, pp. 1359-1369, 2011. · Zbl 1228.34017 · doi:10.1016/j.camwa.2011.03.062
[43] X. Su and S. Zhang, “Unbounded solutions to a boundary value problem of fractional order on the half-line,” Computers & Mathematics with Applications, vol. 61, no. 4, pp. 1079-1087, 2011. · Zbl 1217.34045 · doi:10.1016/j.camwa.2010.12.058