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Nontrivial solutions for a nonlinear multi-point boundary value problem of fractional order. (English) Zbl 1197.34003
Summary: We investigate the existence of nontrivial solutions for a multi-point boundary value problem for fractional differential equations. Under certain growth conditions on the nonlinearity, several sufficient conditions for the existence of nontrivial solution are obtained by using Leray-Schauder nonlinear alternative. As an application, some examples to illustrate our results are given.

MSC:
34A08 Fractional ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
45J05 Integro-ordinary differential equations
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[1] Das, S., Functional fractional calculus for system identification and controls, (2008), Springer New York · Zbl 1154.26007
[2] Kilbas, A.A.; Srivastava, H.M.; Trujillo, J.J., Theory and applications of fractional differential equations, (2006), Elsevier · Zbl 1092.45003
[3] Podlubny, J., Fractional differential equations, (1999), Academic Press New York
[4] Ahmad, B.; Nieto, J.J., Existence of solutions for nonlocal boundary value problems of higher-order nonlinear fractional differential equations, Abstract and applied analysis, 2009, 1-9, (2009) · Zbl 1186.34009
[5] Ahmad, B.; Nieto, J.J., Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions, Computers and mathematics with applications, 58, 1838-1843, (2009) · Zbl 1205.34003
[6] Belmekki, M.; Nieto, J.J.; Rodriguez-Lopez, R., Existence of periodic solution for a nonlinear fractional differential equation, Boundary value problems, 2009, 1-18, (2009) · Zbl 1181.34006
[7] Chang, Y.; Nieto, J.J., Some new existence results for fractional differential inclusions with boundary conditions, Mathematical and computer modelling, 49, 605-609, (2009) · Zbl 1165.34313
[8] Lakshmikantham, V.; Leela, S., Nagumo-type uniqueness result for fractional differential equations, Nonlinear analysis, 71, 2886-2889, (2009) · Zbl 1177.34003
[9] Odibat, Z.; Momani, S., A generalized differential transform method for linear partial differential equations of fractional order, Applied mathematics letters, 21, 194-199, (2008) · Zbl 1132.35302
[10] Rivero, M.; Rodriguez-Germa, L.; Trujillo, J.J., Linear fractional differential equations with variable coefficients, Applied mathematics letters, 21, 892-897, (2008) · Zbl 1152.34305
[11] Guerekata, G.M., Cauchy problem for some fractional abstract differential equation with non local conditions, Nonlinear analysis, 70, 1873-1876, (2009) · Zbl 1166.34320
[12] Li, C.F.; Luo, X.N.; Zhou, Y., Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations, Computers and mathematics with applications, 59, 1363-1375, (2010) · Zbl 1189.34014
[13] Il’in, V.A.; Moiseev, E.I., Nonlocal boundary value problem of the second kind for a Sturm Liouville operator, Differential equations, 23, 8, 979-987, (1987) · Zbl 0668.34024
[14] Il’in, V.A.; Moiseev, E.I., Nonlocal boundary value problem of the first kind for a Sturm Liouville operator in its differential and finite difference aspects, Differential equations, 23, 7, 803-810, (1987) · Zbl 0668.34025
[15] Guo, Y.; Ji, Y.; Zhang, J., Three positive solutions for a nonlinear \(n\)th-order \(m\)-point boundary value problem, Nonlinear analysis, 68, 3485-3492, (2007) · Zbl 1156.34311
[16] Guo, D.; Lakshmikantham, V., Nonlinear problems in abstract cones, (1988), Academic Press Orlando · Zbl 0661.47045
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