×
Zhang, Lihong; Ahmad, Bashir; Wang, Guotao; Agarwal, Ravi P.; Al-Yami, Maryem; Shammakh, Wafa

Nonlocal integrodifferential boundary value problem for nonlinear fractional differential equations on an unbounded domain. (English) Zbl 1470.34035

Abstr. Appl. Anal. 2013, Article ID 813903, 5 p. (2013).
Summary: This paper investigates the existence of nonnegative solutions for nonlinear fractional differential equations with nonlocal fractional integrodifferential boundary conditions on an unbounded domain by means of Leray-Schauder nonlinear alternative theorem. An example is discussed for the illustration of the main work.

Cited in 12 Documents

MSC:

34A08 Fractional ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B40 Boundary value problems on infinite intervals for ordinary differential equations
Cite Review PDF
Full Text: DOI
OA License

References:

[1] Podlubny, I., Fractional Differential Equations, xxiv+340 (1999), San Diego, Calif, USA: Academic Press, San Diego, Calif, USA · Zbl 0924.34008
[2] Zaslavsky, G. M., Hamiltonian Chaos and Fractional Dynamics, xiv+421 (2008), Oxford, UK: Oxford University Press, Oxford, UK · Zbl 1152.37001
[3] Magin, R. L., Fractional Calculus in Bioengineering (2006), Redding, Conn, USA: Begell House, Redding, Conn, USA
[4] Kilbas, A. A.; Srivastava, H. M.; Trujillo, J. J., Theory and Applications of Fractional Differential Equations. Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, 204, xvi+523 (2006), Amsterdam, The Netherlands: Elsevier Science B.V., Amsterdam, The Netherlands · Zbl 1092.45003 · doi:10.1016/S0304-0208(06)80001-0
[5] Sabatier, J.; Agrawal, O. P.; Machado, J. A. T., Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, xiv+552 (2007), Dordrecht, The Netherlands: Springer, Dordrecht, The Netherlands · Zbl 1116.00014 · doi:10.1007/978-1-4020-6042-7
[6] Baleanu, D.; Diethelm, K.; Scalas, E.; Trujillo, J. J., Fractional Calculus Models and Numerical Methods. Fractional Calculus Models and Numerical Methods, Series on Complexity, Nonlinearity and Chaos, xxiv+400 (2012), Boston, Mass, USA: World Scientific, Boston, Mass, USA · Zbl 1248.26011 · doi:10.1142/9789814355216
[7] Lazarević, M. P.; Spasić, A. M., Finite-time stability analysis of fractional order time-delay systems: Gronwall’s approach, Mathematical and Computer Modelling, 49, 3-4, 475-481 (2009) · Zbl 1165.34408 · doi:10.1016/j.mcm.2008.09.011
[8] Ramírez, J. D.; Vatsala, A. S., Monotone iterative technique for fractional differential equations with periodic boundary conditions, Opuscula Mathematica, 29, 3, 289-304 (2009) · Zbl 1267.34011 · doi:10.1155/2012/842813
[9] Zhang, S., Existence results of positive solutions to boundary value problem for fractional differential equation, Positivity, 13, 3, 583-599 (2009) · Zbl 1202.26018
[10] 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 (2009) · Zbl 1186.34009 · doi:10.1155/2009/494720
[11] Wei, Z.; Li, Q.; Che, J., Initial value problems for fractional differential equations involving Riemann-Liouville sequential fractional derivative, Journal of Mathematical Analysis and Applications, 367, 1, 260-272 (2010) · Zbl 1191.34008 · doi:10.1016/j.jmaa.2010.01.023
[12] Ahmad, B.; Ntouyas, S. K., A four-point nonlocal integral boundary value problem for fractional differential equations of arbitrary order, Electronic Journal of Qualitative Theory of Differential Equations, 22, 1-15 (2011) · Zbl 1340.34063
[13] Zhao, Y.; Sun, S.; Han, Z.; Zhang, M., Positive solutions for boundary value problems of nonlinear fractional differential equations, Applied Mathematics and Computation, 217, 16, 6950-6958 (2011) · Zbl 1227.34011 · doi:10.1016/j.amc.2011.01.103
[14] Ahmad, B.; Nieto, J. J., Riemann-Liouville fractional integro-differential equations with fractional nonlocal integral boundary conditions, Boundary Value Problems, 2011, article 36 (2011) · Zbl 1275.45004
[15] Wang, G., Monotone iterative technique for boundary value problems of a nonlinear fractional differential equation with deviating arguments, Journal of Computational and Applied Mathematics, 236, 9, 2425-2430 (2012) · Zbl 1238.65077 · doi:10.1016/j.cam.2011.12.001
[16] Wang, G.; Baleanu, D.; Zhang, L., Monotone iterative method for a class of nonlinear fractional differential equations, Fractional Calculus and Applied Analysis, 15, 2, 244-252 (2012) · Zbl 1273.34021 · doi:10.2478/s13540-012-0018-z
[17] Babakhani, A., Positive solutions for system of nonlinear fractional differential equations in two dimensions with delay, Abstract and Applied Analysis, 2010 (2010) · Zbl 1197.34155 · doi:10.1155/2010/536317
[18] Gafiychuk, V.; Datsko, B.; Meleshko, V.; Blackmore, D., Analysis of the solutions of coupled nonlinear fractional reaction-diffusion equations, Chaos, Solitons & Fractals, 41, 3, 1095-1104 (2009) · Zbl 1198.35123 · doi:10.1016/j.chaos.2008.04.039
[19] Arara, A.; Benchohra, M.; Hamidi, N.; Nieto, J. J., Fractional order differential equations on an unbounded domain, Nonlinear Analysis. Theory, Methods & Applications A, 72, 2, 580-586 (2010) · Zbl 1179.26015 · doi:10.1016/j.na.2009.06.106
[20] Zhao, X.; Ge, W., Unbounded solutions for a fractional boundary value problems on the infinite interval, Acta Applicandae Mathematicae, 109, 2, 495-505 (2010) · Zbl 1193.34008 · doi:10.1007/s10440-008-9329-9
[21] Liang, S.; Zhang, J., 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, 61, 11, 3343-3354 (2011) · Zbl 1235.34079 · doi:10.1016/j.camwa.2011.04.018
[22] Su, X., Solutions to boundary value problem of fractional order on unbounded domains in a Banach space, Nonlinear Analysis. Theory, Methods & Applications A, 74, 8, 2844-2852 (2011) · Zbl 1250.34007 · doi:10.1016/j.na.2011.01.006
[23] Liang, S.; Zhang, J., Existence of multiple positive solutions for \(m\)-point fractional boundary value problems on an infinite interval, Mathematical and Computer Modelling, 54, 5-6, 1334-1346 (2011) · Zbl 1235.34023 · doi:10.1016/j.mcm.2011.04.004
[24] Wang, G.; Ahmad, B.; Zhang, L., A coupled system of nonlinear fractional differential equations with multipoint fractional boundary conditions on an unbounded domain, Abstract and Applied Analysis, 2012 (2012) · Zbl 1242.34010
[25] Liu, Y., Existence and uniqueness of solutions for initial value problems of multi-order fractional differential equations on the half lines, Scientia Sinica Mathematica, 42, 7, 735-756 (2012) · Zbl 1488.34050 · doi:10.1360/012011-1032
[26] Zhang, L.; Ahmad, B.; Wang, G.; Agarwal, R. P., Nonlinear fractional integro-differential equations on unbounded domains in a Banach space, Journal of Computational and Applied Mathematics, 249, 51-56 (2013) · Zbl 1302.45019 · doi:10.1016/j.cam.2013.02.010
[27] Agarwal, R. P.; Meehan, M.; O’Regan, D., Fixed Point Theory and Applications, 141, x+170 (2001), Cambridge, UK: Cambridge University Press, Cambridge, UK · Zbl 0960.54027 · doi:10.1017/CBO9780511543005
[28] Liu, Y., Existence and unboundedness of positive solutions for singular boundary value problems on half-line, Applied Mathematics and Computation, 144, 2-3, 543-556 (2003) · Zbl 1036.34027 · doi:10.1016/S0096-3003(02)00431-9
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.