PL EN


Preferences help
enabled [disable] Abstract
Number of results
Journal
2013 | 11 | 10 | 1399-1413
Article title

Nonlocal Cauchy problems for fractional order nonlinear differential systems

Content
Title variants
Languages of publication
EN
Abstracts
EN
In this paper, we discuss nonlocal Cauchy problems for fractional order nonlinear differential systems. Firstly, an important matrix associated with fractional order and two functionals are constructed. Further, some sufficient conditions which guarantee such matrix convergent to zero matrix are presented. Secondly, by using three fixed point theorems via the techniques that use convergent to zero matrix and vector norm, some existence results for the solutions of such fractional order nonlinear differential systems are given under different conditions. Finally, some examples are given to illustrate the results.
Publisher

Journal
Year
Volume
11
Issue
10
Pages
1399-1413
Physical description
Dates
published
1 - 10 - 2013
online
19 - 12 - 2013
Contributors
author
  • Department of Mathematics, Guizhou University, Guiyang, Guizhou, 550025, P.R. China, xzleemath@126.com
author
  • Department of Mathematics, Xiangtan University, Xiangtan, Hunan, 411105, P.R. China, yzhou@xtu.edu.cn
References
  • [1] D. Baleanu, J. A. T. Machado, A. C.-J. Luo, Fractional Dynamics and Control (Springer, PLACE OF PUBLICATION, 2012) http://dx.doi.org/10.1007/978-1-4614-0457-6[Crossref]
  • [2] K. Diethelm, The Analysis of Fractional Differential Equations (Lecture Notes in Mathematics, PLACE OF PUBLICATION, 2010) http://dx.doi.org/10.1007/978-3-642-14574-2[Crossref]
  • [3] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations (Elsevier Science B.V., Amsterdam, 2006)
  • [4] V. Lakshmikantham, S. Leela, J. V. Devi, Theory of Fractional Dynamic Systems (Cambridge Scientific Publishers, PLACE OF PUBLICATION, 2009)
  • [5] K. S. Miller, B. Ross, An Introduction to the Fractional Calculus and Differential Equations (John Wiley, New York, 1993)
  • [6] M. W. Michalski, Derivatives of Noninteger Order and Their Applications, Dissertationes Mathematicae, CCCXXVIII, (Inst. Math., Polish Acad. Sci., 1993)
  • [7] I. Podlubny, Fractional Differential Equations (Academic Press, San Diego, 1999)
  • [8] V. E. Tarasov, Fractional Dynamics: Application of Fractional Calculus to Dynamics of Particles, Fields and Media (Springer, HEP, 2011)
  • [9] D. Baleanu, K. Diethelm, E. Scalas, J. J. Trujillo, Fractional Calculus Models and Numerical Methods, Series on Complexity, Nonlinearity and Chaos (World Scientific, PLACE OF PUBLICATION, 2012)
  • [10] A. Debbouche, D. Baleanu, R. P. Agarwal, Bound. Value Probl. 2012, 78 (2012) http://dx.doi.org/10.1186/1687-2770-2012-78[Crossref]
  • [11] D. Baleanu, O. G. Mustafa, R. P. Agarwal, Abstr. Appl. Anal. 2010, 865139 (2010)
  • [12] D. Baleanu, O. G. Mustafa, R. P. Agarwal, Comput. Math. Appl. 62, 1492 (2011) http://dx.doi.org/10.1016/j.camwa.2011.03.021[Crossref]
  • [13] D. Baleanu, O. G. Mustafa, R. P. Agarwal, Appl. Math. Lett. 23, 1129 (2010) http://dx.doi.org/10.1016/j.aml.2010.04.049[Crossref]
  • [14] B. Ahmad, J. J. Nieto, Topol. Methods Nonlinear Anal. 35, 295 (2010)
  • [15] Z. Bai, Nonlinear Anal.-Theor. 72, 916 (2010) http://dx.doi.org/10.1016/j.na.2009.07.033[Crossref]
  • [16] M. Benchohra, J. Henderson, S. K. Ntouyas, A. Ouahab, J. Math. Anal. Appl. 338, 1340 (2008) http://dx.doi.org/10.1016/j.jmaa.2007.06.021[Crossref]
  • [17] Y. K. Chang, J. J. Nieto, Math. Comput. Model. 49, 605 (2009) http://dx.doi.org/10.1016/j.mcm.2008.03.014[Crossref]
  • [18] X. Dong, J. Wang, Y. Zhou, Opuscula Math. 31, 341 (2011) http://dx.doi.org/10.7494/OpMath.2011.31.3.341[Crossref]
  • [19] G.M. N’Guérékata, Nonlinear Anal.-Theor. 70, 1873 (2009) http://dx.doi.org/10.1016/j.na.2008.02.087[Crossref]
  • [20] Y. Zhou, F. Jiao, J. Li, Nonlinear Anal.-Theor. 71, 2724 (2009) http://dx.doi.org/10.1016/j.na.2009.01.105[Crossref]
  • [21] Y. Zhou, F. Jiao, Nonlinear Anal.:RWA 11, 4465 (2010) http://dx.doi.org/10.1016/j.nonrwa.2010.05.029[Crossref]
  • [22] F. Jiao, Y. Zhou, Int. J. Bifurcation Chaos 22, 1 (2012)
  • [23] E. Hernández, D. O’Regan, K. Balachandran, Nonlinear Anal.-Theor. 73, 3462 (2010) http://dx.doi.org/10.1016/j.na.2010.07.035[Crossref]
  • [24] M. Fec̆kan, Y. Zhou, J. Wang, Commun. Nonlinear Sci. Numer. Simulat. 17, 3050 (2012) http://dx.doi.org/10.1016/j.cnsns.2011.11.017[Crossref]
  • [25] M. Fec̆kan, J. Wang, Y. Zhou, J. Optim. Theory Appl. 156, 79 (2013) http://dx.doi.org/10.1007/s10957-012-0174-7[Crossref]
  • [26] R. N. Wang, D. H. Chen, T. J. Xiao, J. Differ. Equations 252, 202 (2012) http://dx.doi.org/10.1016/j.jde.2011.08.048[Crossref]
  • [27] K. Li, J. Peng, J. Jia, J. Funct. Anal. 263, 476 (2012) http://dx.doi.org/10.1016/j.jfa.2012.04.011[Crossref]
  • [28] J. Wang, M. Fec̆kan, Y. Zhou, Dynam. Part. Differ. Eq. 8, 345 (2011)
  • [29] J. Wang, M. Fec̆kan, Y. Zhou, Appl. Math. Model. 37, 6055 (2013) http://dx.doi.org/10.1016/j.apm.2012.12.011[Crossref]
  • [30] J. Wang, Y. Zhou, W. Wei, Syst. Control Lett. 61, 472 (2012) http://dx.doi.org/10.1016/j.sysconle.2011.12.009[Crossref]
  • [31] J. Wang, Z. Fan, Y. Zhou, J. Optim. Theory Appl. 154, 292 (2012) http://dx.doi.org/10.1007/s10957-012-9999-3[Crossref]
  • [32] J. Wang, Y. Zhou, M. Fec̆kan, Nonlinear Dyn. 71, 685 (2013) http://dx.doi.org/10.1007/s11071-012-0452-9[Crossref]
  • [33] J. Wang, M. Fec̆kan, Y. Zhou, J. Optim. Theory Appl. 156, 13 (2013) http://dx.doi.org/10.1007/s10957-012-0170-y[Crossref]
  • [34] S. Kumar, N. Sukavanam, J. Differ. Equations 252, 6163 (2012) http://dx.doi.org/10.1016/j.jde.2012.02.014[Crossref]
  • [35] C. Bai, J. Fang, Appl. Math. Comput. 150, 611 (2004) http://dx.doi.org/10.1016/S0096-3003(03)00294-7[Crossref]
  • [36] B. Ahmad, J. J. Nieto, Comput. Math. Appl. 58, 1838 (2009) http://dx.doi.org/10.1016/j.camwa.2009.07.091[Crossref]
  • [37] X. Su, Appl. Math. Lett. 22, 64 (2009) http://dx.doi.org/10.1016/j.aml.2008.03.001[Crossref]
  • [38] Z. M. Odibat, Comput. Math. Appl. 59, 1171 (2010) http://dx.doi.org/10.1016/j.camwa.2009.06.035[Crossref]
  • [39] D. Qian, C. Li, R. P. Agarwal, P. J. Y. Wong, Math. Comput. Model. 52, 862 (2010) http://dx.doi.org/10.1016/j.mcm.2010.05.016[Crossref]
  • [40] S. Sun, Q. Li, Y. Li, Comput. Math. Appl. 64, 3310 (2012) http://dx.doi.org/10.1016/j.camwa.2012.01.065[Crossref]
  • [41] O. Nica, Fixed Point Theory 13, 603 (2012)
  • [42] O. Nica, R. Precup, Stud. Univ. Babes-Bolyai Math. 56, 125 (2011)
  • [43] R. Precup, Math. Comp. Model. 49, 703 (2009) http://dx.doi.org/10.1016/j.mcm.2008.04.006[Crossref]
  • [44] R. Precup, Methods in Nonlinear Integral Equations (Kluwer, Dordrecht, 2002) http://dx.doi.org/10.1007/978-94-015-9986-3[Crossref]
  • [45] R. P. Agarwal, M. Meehan, D. O’Regan, Fixed Point Theory and Applications (Cambridge University Press, Cambridge, 2001) http://dx.doi.org/10.1017/CBO9780511543005[Crossref]
  • [46] A. Granas, J. Dugundji, Fixed Point Theory (Springer, New York, 2003) http://dx.doi.org/10.1007/978-0-387-21593-8[Crossref]
  • [47] D. O’Regan, R. Precup, Theorems of Leray-Schauder Type and Applications (Gordon and Breach, Amsterdam, 2001)
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.-psjd-doi-10_2478_s11534-013-0233-1
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.