Stability regions for linear fractional differential systems and their discretizations

Applied Mathematics and Computation

Volumn 219, Issue 12, 2013, Pages 7012-7022

  Čermák, Jan ^a   Kisela, Tomáš ^a   Nechvátal, Luděk ^a  

^a BRNO UNIVERSITY OF TECHNOLOGY   (Czech Republic)

Author keywords

Asymptotic stability; Fractional difference system; Fractional differential system; Laplace transform

Indexed keywords

ASYMPTOTICS; BACKWARD DIFFERENCE; DERIVATIVE OPERATORS; DIFFERENCE SYSTEMS; DISCRETIZATIONS; FRACTIONAL DIFFERENTIAL; PROOF TOOLS; QUALITATIVE PROPERTIES; STABILITY PROPERTIES; STABILITY REGIONS;

ASYMPTOTIC STABILITY; LAPLACE TRANSFORMS;

DIFFERENTIAL EQUATIONS;

EID: 84874100688     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2012.12.019     Document Type: Article

References (28)

1. R.P. Agarwal Certain fractional q-integrals and q-derivatives Proc. Camb. Philos. Soc. 66 1969 365 370
2. W.A. Al-Salam Some fractional q-integrals and q-derivatives Proc. Edin. Math. Soc. 15 1966 135 140
3. J.A.D. Appleby, I. Gyri, and D.W. Reynolds On exact convergence rates for solutions of linear systems of Volterra difference equations J. Differ. Equ. Appl. 12 12 2006 1257 1275
4. F.M. Atici, and P.W. Eloe A transform method in discrete fractional calculus Int. J. Differ. Equ. 2 2007 165 176
5. F.M. Atici, and P.W. Eloe Discrete fractional calculus with the nabla operator Electron. J. Qual. Theory Differ. Equ. 3 2009 1 12 Spec. Ed.
6. F.M. Atici, and P.W. Eloe Linear systems of fractional nabla difference equations Rocky Mountain J. Math. 41 2 2011 353 370
7. M. Bohner, and A. Peterson Advances in Dynamic Equations on Time Scales 2003 Birkhäuser Boston, MA
8. M. Bohner, and G.Sh. Guseinov The h-Laplace and q-Laplace transforms J. Math. Anal. Appl. 365 2010 75 92
9. J. Čermák, T. Kisela, and L. Nechvátal Discrete Mittag-Leffler functions in linear fractional difference equations Abstr. Appl. Anal. 2011 2011 21 p., Article ID 565067
10. J. Čermák, T. Kisela, and L. Nechvátal Stability and asymptotic properties of a linear fractional difference equation Adv. Differ. Equ. 122 2012 10.1186/1687-1847-2012-122 16 p.
11. J. Čermák, and L. Nechvátal On (q, h) -analogue of fractional calculus J. Nonlinear Math. Phys. 17 1 2010 51 68
12. C.A. Desoer, and M. Vidyassager Feedback Systems: Input-Output Properties 1975 Academic Press New York
13. J. Diblík, and E. Schmeidel On the existence of solutions of linear Volterra difference equations asymptotically equivalent to a given sequence Appl. Math. Comput. 218 18 2012 9310 9320
14. R. Díaz, and E. Pariguan On hypergeometric functions and k-Pochhammer symbol Divulg. Mat. 15 2 2007 179 192
15. L. Galeone, and R. Garrappa On multistep methods for differential equations of fractional order Mediterr. J. Math. 3 2006 565 580
16. T.W. Gamelin Complex Analysis 2001 Springer New-York
17. K. Knopp Infinite Sequences and Series 1956 Dover Publ. New York
18. C. Lubich Fractional linear multistep methods for Abel-Volterra integral equations of the second kind Math. Comput. 45 1985 463 469
19. C. Lubich A stability analysis of convolution quadratures for Abel-Volterra integral equations IMA J. Numer. Anal. 6 1986 87 101
20. K.S. Miller, and B. Ross An Introduction to the Fractional Calculus and Fractional Differential Equations 1993 John Wiley & Sons Inc. New York
21. A. Nagai Discrete Mittag-Leffler function and its applications Publ. Res. Inst. Math. Sci. Kyoto Univ. 1302 2003 1 20
22. J.J. Nieto Maximum principles for fractional differential equations derived from Mittag-Leffler functions Appl. Math. Lett. 23 2010 1248 1251
23. K.B. Oldham, and J. Spanier The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order 2006 Dover Publications, Inc.
24. J. Peng, and K. Li A note on property of the Mittag-Leffler function J. Math. Anal. Appl. 370 2010 635 638
25. I. Podlubny Fractional Differential Equations 1999 Academic Press New York
26. D. Qian, Ch. Li, R.P. Agarwal, and P.J.Y. Wong Stability analysis of fractional differential system with Riemann-Liouville derivative Math. Comput. Model. 52 5-6 2010 862 874
27. M. Rivero, J.J. Trujillo, L. Vázquez, and M.P. Velasco Fractional dynamics of populations Appl. Math. Comput. 218 2011 1089 1095
28. V.E. Tarasov Fractional generalization of gradient and Hamiltonian systems J. Phys. A.: Math. Gen. 38 2005 5929 5943