Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
In this article, we discuss existence, uniqueness and dependency of solutions of nonlinear fractional nabla difference equations in a Banach space equipped with a suitable norm, using the contractive mapping approach. As an application of the established results we present and analyse a few examples.
Czasopismo
Rocznik
Tom
Strony
215--238
Opis fizyczny
Bibliogr. 24 poz.
Twórcy
autor
- Department of Mathematics Birla Institute of Technology and Science Pilani Hyderabad Campus Hyderabad - 500078, Telangana, India
Bibliografia
- [1] T. Abdeljawad, On Riemann and Caputo fractional differences, Computers and Mathematics with Applications 62 (2011), 1602-1611.
- [2] T. Abdeljawad, F.M. Atici, On the definitions of nabla fractional operators, Abstract and Applied Analysis 2012, Article ID 406757, 13 pp.
- [3] N. Acar, F.M. Atici, Exponential functions of discrete fractional calculus, Applicable Analysis and Discrete Mathematics 7 (2013), 343-353.
- [4] R.P. Agarwal, Difference Equations and Inequalities, Marcel Dekker, New York, 1992.
- [5] G.A. Anastassiou, Nabla discrete fractional calculus and nabla inequalities, Mathematical and Computer Modelling 51 (2010), 562-571.
- [6] F.M. Atici, P.W. Eloe, Discrete fractional calculus with the nabla operator, Electron. J. Qual. Theory Differ. Equat., Special Edition I (2009), Number 13, 12 pp.
- [7] F.M. Atici, P.W. Eloe, Gronwall's inequality on discrete fractional calculus, Computers and Mathematics with Applications 64 (2012), 3193-3200.
- [8] F.M. Atici, P.W. Eloe, Linear systems of nabla fractional difference equations, Rocky Mountain Journal of Mathematics 41 (2011) 2, 353-370.
- [9] M. Bohner, A. Peterson, Dynamic Equations on Time Scales, Birkhauser, Boston, 2001.
- [10] M. Bohner, A. Peterson, Advances in Dynamic Equations on Time Scales, Birkhauser, Boston, 2002.
- [11] J. Cermak, T. Kisela, L. Nechvatal, Stability and asymptotic properties of a linear fractional difference equation, Advances in Difference Equations 2012, 2012:122, DOL10.1186/1687-1847-2012-122.
- [12] Fulai Chen, Xiannan Luo, Yong Zhou, Existence results for nonlinear fractional difference equation, Advances in Difference Equations, 2011, Article ID 713201, 12 pp.
- [13] S. Elaydi, An Introduction to Difference Equations, 3rd ed., Springer, New York, 2005.
- [14] H.L. Gray, N.F. Zhang, On a new definition of the fractional difference, Mathematics of Computation 50 (1988) 182, 513-529.
- [15] J. Hein, S. McCarthy, N. Gaswick, B. McKain, K. Spear, Laplace transforms for the nabla difference operator, Pan American Mathematical Journal 21 (2011) 3, 79-96.
- [16] J. Jagan Mohan, G.V.S.R. Deekshitulu, Solutions of nabla fractional difference equations using N-transforms, Commun. Math. Stat. 2 (2014), 1-16.
- [17] J. Jagan Mohan, N. Shobanadevi, G.V.S.R. Deekshitulu, Stability of nonlinear nabla fractional difference equations using fixed point theorems, Italian Journal of Pure and Applied Mathematics 32 (2014), 165-184.
- [18] J.M. Jonnalagadda, Analysis of nonlinear fractional nabla difference equations, International Journal of Analysis and Applications 7 (2015) 1, 79-95.
- [19] J. Jonnalagadda, Analysis of a system of nonlinear fractional nabla difference equations, Int. J. Dynamical Systems and Differential Equations 5 (2015) 2, 149-174.
- [20] A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, North - Holland Mathematics Studies, Elsevier Science B.V., Amsterdam, The Netherlands, 2006.
- [21] E. Kreyszig, Introductory Functional Analysis with Applications, John Wiley and Sons, Canada, 1978.
- [22] A. Nagai, Discrete Mittag-Leffler function and its applications, Publ. Res. Inst. Math. Sci., Kyoto Univ. 1302 (2003), 1-20.
- [23] K.S. Miller, B. Ross, Fractional difference calculus, Proceedings of the International Symposium on Univalent Functions, Fractional Calculus and Their Applications, 139-152, Nihon University, Koriyama, Japan, 1989.
- [24] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
Uwagi
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-67e0ad34-d4ad-4172-8418-9363bccdfb50