Monotone iterative procedure and systems of a finite number of nonlinear fractional differential equations
| dc.contributor.author | Wardowski, Dariusz | |
| dc.date.accessioned | 2015-09-03T13:04:58Z | |
| dc.date.available | 2015-09-03T13:04:58Z | |
| dc.date.issued | 2015-06-03 | |
| dc.identifier.issn | 1687-1847 | |
| dc.identifier.uri | http://hdl.handle.net/11089/11661 | |
| dc.description.abstract | The aim of the paper is to present a nontrivial and natural extension of the comparison result and the monotone iterative procedure based on upper and lower solutions, which were recently established in (Wang et al. in Appl. Math. Lett. 25:1019-1024, 2012), to the case of any finite number of nonlinear fractional differential equations. | pl_PL |
| dc.description.sponsorship | The author is very grateful to the reviewers for the remarks, which improved the final version of the manuscript. This article was financially supported by University of Łódź as a part of donation for the research activities aimed at the development of young scientists, grant no. 545/1117. | pl_PL |
| dc.language.iso | en | pl_PL |
| dc.publisher | Springer International Publishing | pl_PL |
| dc.relation.ispartofseries | Advances in Difference Equations;2015 | |
| dc.rights | Uznanie autorstwa 3.0 Polska | * |
| dc.rights.uri | http://creativecommons.org/licenses/by/3.0/pl/ | * |
| dc.title | Monotone iterative procedure and systems of a finite number of nonlinear fractional differential equations | pl_PL |
| dc.type | Article | pl_PL |
| dc.page.number | 1-16 | pl_PL |
| dc.contributor.authorAffiliation | Department of Nonlinear Analysis, Faculty of Mathematics and Computer Science, University of Łódź | pl_PL |
| dc.references | Babakhani, A, Daftardar-Gejji, V: Existence of positive solutions of nonlinear fractional differential equations. J. Math. Anal. Appl. 278, 434-442 (2003) | pl_PL |
| dc.references | Bai, ZB: On positive solutions of a nonlocal fractional boundary value problem. Nonlinear Anal. 72, 916-924 (2010) | pl_PL |
| dc.references | Bai, ZB, Lu, HS: Positive solutions of boundary value problems of nonlinear fractional differential equation. J. Math. Anal. Appl. 311, 495-505 (2005) | pl_PL |
| dc.references | Belmekki, M, Benchohra, M: Existence results for fractional order semilinear functional differential equations with nondense domain. Nonlinear Anal. 72, 925-932 (2010) | pl_PL |
| dc.references | Belmekki, M, Nieto, JJ, Rodriguez-Lopez, R: Existence of periodic solution for a nonlinear fractional differential equation. Bound. Value Probl. 2009, Article ID 324561 (2009) | pl_PL |
| dc.references | El-Shahed, M: Positive solutions for boundary value problem of nonlinear fractional differential equation. Abstr. Appl. Anal. 2007, Article ID 10368 (2007) | pl_PL |
| dc.references | Lakshmikantham, V, Vatsala, AS: Basic theory of fractional differential equations. Nonlinear Anal. 69(8), 2677-2682 (2008) | pl_PL |
| dc.references | Lakshmikanthan, V, Vatsala, AS: General uniqueness and monotone iterative technique for fractional differential equations. Appl. Math. Lett. 21, 828-834 (2008) | pl_PL |
| dc.references | McRae, FA: Monotone iterative technique and existence results for fractional differential equations. Nonlinear Anal. 71, 6093-6096 (2009) | pl_PL |
| dc.references | Wang, G, Agarwal, RP, Cabada, A: Existence results and the monotone iterative technique for systems of nonlinear fractional differential equations. Appl. Math. Lett. 25, 1019-1024 (2012) | pl_PL |
| dc.references | Wei, Z, Li, Q, Che, J: Initial value problems for fractional differential equations involving Riemann-Liouville sequential fractional derivative. J. Math. Anal. Appl. 367, 260-272 (2010) | pl_PL |
| dc.references | Zhang, S: Monotone iterative method for initial value problem involving Riemann-Liouville fractional derivatives. Nonlinear Anal. 71, 2087-2093 (2009) | pl_PL |
| dc.references | Zhang, S: The existence of a positive solution for a nonlinear fractional differential equation. J. Math. Anal. Appl. 252, 804-812 (2000) | pl_PL |
| dc.references | Ahmad, B, Nieto, JJ: Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions. Comput. Math. Appl. 58, 1838-1843 (2009) | pl_PL |
| dc.references | Bai, C, Fang, J: The existence of a positive solution for a singular coupled system of nonlinear fractional differential equations. Appl. Math. Comput. 150, 611-621 (2004) | pl_PL |
| dc.references | Bhalekar, S, Daftardar-Gejji, V: Fractional ordered Liu system with time-delay. Commun. Nonlinear Sci. Numer. Simul. 15, 2178-2191 (2010) | pl_PL |
| dc.references | Chen, Y, An, H: Numerical solutions of coupled Burgers equations with time and space fractional derivatives. Appl. Math. Comput. 200, 87-95 (2008) | pl_PL |
| dc.references | Daftardar-Gejji, V: Positive solutions of a system of non-autonomous fractional differential equations. J. Math. Anal. Appl. 302, 56-64 (2005) | pl_PL |
| dc.references | Gafiychuk, V, Datsko, B, Meleshko, V: Mathematical modeling of time fractional reaction-diffusion systems. J. Comput. Appl. Math. 220, 215-225 (2008) | pl_PL |
| dc.references | Jafari, H, Daftardar-Gejji, V: Solving a system of nonlinear fractional differential equations using Adomian decomposition. J. Comput. Appl. Math. 196, 644-651 (2006) | pl_PL |
| dc.references | Lazarevi, MP: Finite time stability analysis of PDα fractional control of robotic time-delay systems. Mech. Res. Commun. 33, 269-279 (2006) | pl_PL |
| dc.references | Su, X: Boundary value problem for a coupled system of nonlinear fractional differential equations. Appl. Math. Lett. 22, 64-69 (2009) | pl_PL |
| dc.references | Kilbas, AA, Srivastava, HM, Trujillo, JJ: Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, vol. 204. Elsevier, Amsterdam (2006) | pl_PL |
| dc.references | Podlubny, I: Fractional Differential Equations. Mathematics in Science and Engineering. Academic Press, New York (1999) | pl_PL |
| dc.references | Samko, SG, Kilbas, AA, Marichev, OI: Fractional Integrals and Derivatives: Theory and Applications. Gordon & Breach, Yverdon (1993) | pl_PL |
| dc.contributor.authorEmail | wardd@math.uni.lodz.pl | pl_PL |
| dc.identifier.doi | 10.1186/s13662-015-0504-9 | |
| dc.relation.volume | 167 | pl_PL |
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