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Wang, Guotao; Liu, Sanyang; Baleanu, Dumitru; Zhang, Lihong

A new impulsive multi-orders fractional differential equation involving multipoint fractional integral boundary conditions. (English) Zbl 1474.34056

Abstr. Appl. Anal. 2014, Article ID 932747, 10 p. (2014).
Summary: A new impulsive multi-orders fractional differential equation is studied. The existence and uniqueness results are obtained for a nonlinear problem with fractional integral boundary conditions by applying standard fixed point theorems. An example for the illustration of the main result is presented.

Cited in 6 Documents

MSC:

34A08 Fractional ordinary differential equations
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\textit{G. Wang} et al., Abstr. Appl. Anal. 2014, Article ID 932747, 10 p. (2014; Zbl 1474.34056)
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References:

[1] 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, Amsterdam, The Netherlands · Zbl 1092.45003
[2] Lakshmikantham, V.; Leela, S.; Devi, J. V., Theory of Fractional Dynamic Systems (2009), Cambridge, UK: Cambridge Scientific Publishers, Cambridge, UK · Zbl 1188.37002
[3] Sabatier, J.; Agrawal, O. P.; Machado, J. A. T., Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering (2007), Dordrecht, The Netherlands: Springer, Dordrecht, The Netherlands · Zbl 1116.00014
[4] 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, 3 (2012), Boston, Mass, USA: World Scientific, Boston, Mass, USA · Zbl 1248.26011
[5] Dinç, E.; Baleanu, D., Fractional wavelet transform for the quantitative spectral resolution of the composite signals of the active compounds in a two-component mixture, Computers & Mathematics with Applications, 59, 5, 1701-1708 (2010) · Zbl 1189.94028
[6] Ahmad, B.; Sivasundaram, S., Existence results for nonlinear impulsive hybrid boundary value problems involving fractional differential equations, Nonlinear Analysis: Hybrid Systems, 3, 3, 251-258 (2009) · Zbl 1193.34056
[7] Debbouche, A.; Baleanu, D., Controllability of fractional evolution nonlocal impulsive quasilinear delay integro-differential systems, Computers & Mathematics with Applications, 62, 3, 1442-1450 (2011) · Zbl 1228.45013
[8] Tian, Y.; Bai, Z., Existence results for the three-point impulsive boundary value problem involving fractional differential equations, Computers & Mathematics with Applications, 59, 8, 2601-2609 (2010) · Zbl 1193.34007
[9] Mophou, G. M., Existence and uniqueness of mild solutions to impulsive fractional differential equations, Nonlinear Analysis: Theory, Methods & Applications, 72, 3-4, 1604-1615 (2010) · Zbl 1187.34108
[10] Bai, C., Impulsive periodic boundary value problems for fractional differential equation involving Riemann-Liouville sequential fractional derivative, Journal of Mathematical Analysis and Applications, 384, 2, 211-231 (2011) · Zbl 1234.34005
[11] Zhang, L.; Wang, G.; Song, G., Existence of solutions for nonlinear impulsive fractional differentia equations of order \(\alpha \in \) (2, 3] with nonlocal boundary conditions, Abstract and Applied Analysis, 2012 (2012) · Zbl 1246.34014
[12] Zhang, L.; Wang, G., Existence of solutions for nonlinear fractional differential equations with impulses and anti-periodic boundary conditions, Electronic Journal of Qualitative Theory of Differential Equations, 7, 1-11 (2011) · Zbl 1261.34015
[13] Liu, Z.; Lu, L.; Szántó, I., Existence of solutions for fractional impulsive differential equations with \(p\)-Laplacian operator, Acta Mathematica Hungarica, 141, 3, 203-219 (2013) · Zbl 1313.34242
[14] Zhang, X.; Huang, X.; Liu, Z., The existence and uniqueness of mild solutions for impulsive fractional equations with nonlocal conditions and infinite delay, Nonlinear Analysis: Hybrid Systems, 4, 4, 775-781 (2010) · Zbl 1207.34101
[15] Balachandran, K.; Kiruthika, S.; Trujillo, J. J., Existence results for fractional impulsive integrodifferential equations in Banach spaces, Communications in Nonlinear Science and Numerical Simulation, 16, 4, 1970-1977 (2011) · Zbl 1221.34215
[16] Agarwal, R. P.; Benchohra, M.; Hamani, S., A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions, Acta Applicandae Mathematicae, 109, 3, 973-1033 (2010) · Zbl 1198.26004
[17] Bouzaroura, A.; Mazouzi, S., An alternative method for the study of impulsive differential equations of fractional orders in a Banach space, International Journal of Differential Equations, 2013 (2013) · Zbl 1295.34009
[18] Wang, G.; Ahmad, B.; Zhang, L., Impulsive anti-periodic boundary value problem for nonlinear differential equations of fractional order, Nonlinear Analysis: Theory, Methods & Applications, 74, 3, 792-804 (2011) · Zbl 1214.34009
[19] Wang, G.; Ahmad, B.; Zhang, L., On nonlocal integral boundary value problems for impulsive non-linear differential equations of fractional order, Fixed Point Theory, 15, 265-284 (2014) · Zbl 1312.34027
[20] Fečkan, M.; Zhou, Y.; Wang, J. R., On the concept and existence of solution for impulsive fractional differential equations, Communications in Nonlinear Science and Numerical Simulation, 17, 7, 3050-3060 (2012) · Zbl 1252.35277
[21] Chauhan, A.; Dabas, J., Local and global existence of mild solution to an impulsive fractional functional integro-differential equation with nonlocal condition, Communications in Nonlinear Science and Numerical Simulation, 19, 4, 821-829 (2014) · Zbl 1457.45004
[22] Zhou, X.-F.; Liu, S.; Jiang, W., Complete controllability of impulsive fractional linear time-invariant systems with delay, Abstract and Applied Analysis, 2013 (2013) · Zbl 1291.34129
[23] Wang, G.; Ahmad, B.; Zhang, L., Some existence results for impulsive nonlinear fractional differential equations with mixed boundary conditions, Computers & Mathematics with Applications, 62, 3, 1389-1397 (2011) · Zbl 1228.34021
[24] Wang, G.; Ahmad, B.; Zhang, L.; Nieto, J. J., Comments on the concept of existence of solution for impulsive fractional differential equations, Communications in Nonlinear Science and Numerical Simulation, 19, 3, 401-403 (2014) · Zbl 1470.34031
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