PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2013 | 11 | 10 | 1377-1386
Tytuł artykułu

Existence and approximation of solutions of fractional order iterative differential equations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we investigate existence and approximation of solutions of fractional order iterative differential equations by virtue of nonexpansive mappings, fractional calculus and fixed point methods. Three existence theorems as well as convergence theorems for a fixed point iterative method designed to approximate these solutions are obtained in two different work spaces via Chebyshev’s norm, Bielecki’s norm and β norm. Finally, an example is given to illustrate the obtained results.
Wydawca

Czasopismo
Rocznik
Tom
11
Numer
10
Strony
1377-1386
Opis fizyczny
Daty
wydano
2013-10-01
online
2013-12-19
Twórcy
autor
  • Department of Mathematics, Guizhou University Guiyang, Guizhou, 550025, P.R. China, jhdengmath@126.com
Bibliografia
  • [1] C. T. Kelley, Iterative methods for linear and nonlinear equations (Society for Industrial and Applied Mathematics, Philadelphia, 1995) http://dx.doi.org/10.1137/1.9781611970944[Crossref]
  • [2] K. Wang, Funkcialaj Ekvacioj 33, 405 (1990)
  • [3] M. Medveď, Ann. Polonici Math. LIV. 3, 263 (1991)
  • [4] M. Fečkan, Math. Slovaca 43, 39 (1993)
  • [5] J. Si, Xi. Wang, J. Math. Anal. Appl. 226, 377 (1998) http://dx.doi.org/10.1006/jmaa.1998.6086[Crossref]
  • [6] S. Stanek, Funct. Diff. Eqs. 5, 463 (1998)
  • [7] J. Liu, Results Math. 55, 129 (2009) http://dx.doi.org/10.1007/s00025-009-0388-7[Crossref]
  • [8] E. Egri, I. A. Rus, Mathematica 52, 67 (2007)
  • [9] V. Muresan, Novi Sad J. Math. 33, 1 (2003)
  • [10] V. Berinde, Miskolc Math. Notes 11, 13 (2010)
  • [11] M. Lauran, Filomat, 25, 21 (2011) http://dx.doi.org/10.2298/FIL1102021L[Crossref]
  • [12] D. Baleanu, J. A. T. Machado, A.C.-J. Luo, Fractional dynamics and control (Springer, Berlin, 2012) http://dx.doi.org/10.1007/978-1-4614-0457-6[Crossref]
  • [13] K. Diethelm, Lect. Notes Math. 2004 (2010)
  • [14] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations (Elsevier Science B.V., Amsterdam, 2006)
  • [15] V. Lakshmikantham, S. Leela, J. V. Devi, Theory of fractional dynamic systems (Cambridge Scientific Publishers, Cambridge, 2009)
  • [16] K. S. Miller, B. Ross, An introduction to the fractional calculus and differential equations (John Wiley, New York, 1993)
  • [17] M. W. Michalski, Derivatives of noninteger order and their applications, Dissertationes Mathematicae, CCCXXVIII (Inst. Math., Polish Acad. Sci., Warsaw, 1993)
  • [18] I. Podlubny, Fractional differential equations (Academic Press, New York, 1999)
  • [19] V. E. Tarasov, Fractional dynamics: Application of fractional calculus to dynamics of particles, fields and media (Springer, HEP, New York, 2011)
  • [20] D. Baleanu, K. Diethelm, E. Scalas, J. J. Trujillo, Fractional calculus models and numerical methods, Series on complexity, nonlinearity and chaos (World Scientific, Singapore, 2012)
  • [21] S. Abbas, M. Benchohra, G. M. N’Guérékata, Topics in fractional differential equations (Springer, 2012) http://dx.doi.org/10.1007/978-1-4614-4036-9[Crossref]
  • [22] J. Klafter, S. C. Lim, R. Metzler, Fractional dynamics in physics: Recent advances (World Scientific, Singapore, 2012)
  • [23] A. Debbouche, D. Baleanu, R. P. Agarwal, Bound. Value Probl. 2012, 78 (2012) http://dx.doi.org/10.1186/1687-2770-2012-78[Crossref]
  • [24] D. Baleanu, O. G. Mustafa, R. P. Agarwal, Abstr. Appl. Anal. 2010, 865139 (2010)
  • [25] 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]
  • [26] 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]
  • [27] B. Ahmad, J. J. Nieto, Topol. Methods Nonlinear Anal. 35, 295 (2010)
  • [28] Z. Bai, Nonlinear Anal.:TMA 72, 916 (2010) http://dx.doi.org/10.1016/j.na.2009.07.033[Crossref]
  • [29] Y. K. Chang, J. J. Nieto, Math. Comput. Model. 49, 605 (2009) http://dx.doi.org/10.1016/j.mcm.2008.03.014[Crossref]
  • [30] Y. Zhou, F. Jiao, Nonlinear Analysis:RWA 11, 4465 (2010) http://dx.doi.org/10.1016/j.nonrwa.2010.05.029[Crossref]
  • [31] E. Hernández, D. O’Regan, K. Balachandran, Nonlinear Anal.:TMA 73, 3462 (2010) http://dx.doi.org/10.1016/j.na.2010.07.035[Crossref]
  • [32] M. Fečkan, Y. Zhou, J. Wang, Commun. Nonlinear Sci. Numer. Simulat. 17, 3050 (2012) http://dx.doi.org/10.1016/j.cnsns.2011.11.017[Crossref]
  • [33] J. Wang, M. Fečkan, Y. Zhou, Appl. Math. Model. 37, 6055 (2013) http://dx.doi.org/10.1016/j.apm.2012.12.011[Crossref]
  • [34] J. Wang, M. Fečkan, Y. Zhou, J. Optim. Theory Appl. 156, 13 (2013) http://dx.doi.org/10.1007/s10957-012-0170-y[Crossref]
  • [35] T. F. Nonnenmacher, W. G. Glockle, Philosophical Magazine Letters 64, 89 (1991) http://dx.doi.org/10.1080/09500839108214672[Crossref]
  • [36] H. Schiessel, A. Blumen, J. Physics A: Mathematical and General 26, 5057 (1993) http://dx.doi.org/10.1088/0305-4470/26/19/034[Crossref]
  • [37] T. F. Nonnenmacher, R. Metzler, Applications of fractional calculus techniques to problems in biophysics, Applications of Fractional Calculus in Physics (World Scientific Publishing, Singapore, 2000) 377 http://dx.doi.org/10.1142/9789812817747_0008[Crossref]
  • [38] R. Metzler, T. F. Nonnenmacher, Int. J. Plasticity 19, 941 (2003) http://dx.doi.org/10.1016/S0749-6419(02)00087-6[Crossref]
  • [39] S. M. Jung, T. S. Kim, K. S. Lee, Bull. Korean Math. Soc. 43, 531 (2006) http://dx.doi.org/10.4134/BKMS.2006.43.3.531[Crossref]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.-psjd-doi-10_2478_s11534-013-0270-9
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.