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**Solvability for a coupled system of fractional integrodifferential equations with \(m\)-point boundary conditions on the half-line.**
*(English)*
Zbl 1469.34039

Summary: The aim of this paper is to study the solvability for a coupled system of fractional integrodifferential equations with multipoint fractional boundary value problems on the half-line. An example is given to demonstrate the validity of our assumptions.

### MSC:

34B10 | Nonlocal and multipoint boundary value problems for ordinary differential equations |

34A08 | Fractional ordinary differential equations |

34B40 | Boundary value problems on infinite intervals for ordinary differential equations |

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\textit{P. Nasertayoob} et al., Abstr. Appl. Anal. 2014, Article ID 297314, 7 p. (2014; Zbl 1469.34039)

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### References:

[1] | Hilfer, R., Applications of Fractional Calculus in Physics (2000), Singapore: World Scientific Publishing, Singapore · Zbl 0998.26002 |

[2] | 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 (2006), Amsterdam, The Netherlands: Elsevier Science B. V., Amsterdam, The Netherlands · Zbl 1092.45003 |

[3] | Lakshmikantham, V.; Leela, S.; Devi, J. V., Theory of Fractional Dynamic Systems (2009), Cambridge, UK: Cambridge Scientific Publishers, Cambridge, UK · Zbl 1188.37002 |

[4] | Ahmad, B.; Nieto, J. J., Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions, Computers & Mathematics with Applications, 58, 9, 1838-1843 (2009) · Zbl 1205.34003 |

[5] | Bai, C.; Fang, J., The existence of a positive solution for a singular coupled system of nonlinear fractional differential equations, Applied Mathematics and Computation, 150, 3, 611-621 (2004) · Zbl 1061.34001 |

[6] | Chen, Y.; Chen, D.; Lv, Z., The existence results for a coupled system of nonlinear fractional differential equations with multi-point boundary conditions, Bulletin of the Iranian Mathematical Society, 38, 3, 607-624 (2012) · Zbl 1298.34011 |

[7] | Gaber, M.; Brikaa, M. G., Existence results for a coupled system of nonlinear fractional differential equation with four-point boundary conditions, ISRN Mathematical Analysis, 2011 (2011) · Zbl 1241.34009 |

[8] | Khodabakhshi, N.; Vaezpour, S. M., Existence results for a coupled system of nonlinear fractional differential equations with boundary value problems on an unbounded domain, Electronic Journal of Qualitative Theory of Differential Equations, 73 (2013) · Zbl 1340.34019 |

[9] | Su, X., Boundary value problem for a coupled system of nonlinear fractional differential equations, Applied Mathematics Letters. An International Journal of Rapid Publication, 22, 1, 64-69 (2009) · Zbl 1163.34321 |

[10] | 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 |

[11] | Wang, J.; Xiang, H.; Liu, Z., Positive solution to nonzero boundary values problem for a coupled system of nonlinear fractional differential equations, International Journal of Differential Equations, 2010 (2010) · Zbl 1207.34012 |

[12] | Yang, W., Positive solutions for a coupled system of nonlinear fractional differential equations with integral boundary conditions, Computers & Mathematics with Applications, 63, 1, 288-297 (2012) · Zbl 1238.34047 |

[13] | Yuan, C., Two positive solutions for \((n-1, 1)\)-type semipositone integral boundary value problems for coupled systems of nonlinear fractional differential equations, Communications in Nonlinear Science and Numerical Simulation, 17, 2, 930-942 (2012) · Zbl 1248.35225 |

[14] | Anguraj, A.; Karthikeyan, P.; N’Guereata, G., Nonlocal Cauchy problem for some fractional abstract integro-differential equations in Banach spaces, Communications in Mathematical Analysis, 6, 1, 31-35 (2009) · Zbl 1167.34387 |

[15] | Ahmad, B.; Sivasundaram, S., Some existence results for fractional integro-differential equations with nonlinear conditions, Communications in Applied Analysis, 12, 2, 107-112 (2008) · Zbl 1179.45009 |

[16] | Balachandran, K.; Trujillo, J. J., The nonlocal Cauchy problem for nonlinear fractional integrodifferential equations in Banach spaces, Nonlinear Analysis: Theory, Methods and Applications, 72, 12, 4587-4593 (2010) · Zbl 1196.34007 |

[17] | Nazari, D.; Shahmorad, S., Application of the fractional differential transform method to fractional-order integro-differential equations with nonlocal boundary conditions, Journal of Computational and Applied Mathematics, 234, 3, 883-891 (2010) · Zbl 1188.65174 |

[18] | Wang, J.; Yan, X.; Zhang, X. H.; Wang, T. M.; Li, X. Z., A class of nonlocal integrodifferential equations via fractional derivative and its mild solutions, Opuscula Mathematica, 31, 1, 119-135 (2011) · Zbl 1235.34210 |

[19] | 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 |

[20] | 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 |

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