Basics of Riemann delta and nabla integration on time scales

Journal of Difference Equations and Applications

Volumn 8, Issue 11, 2002, Pages 1001-1017

  Guseinov, G Sh ^a   Kaymakalan B ^b  

^a ATILIM UNIVERSITY   (Turkey)

^b GEORGIA SOUTHERN UNIVERSITY   (United States)

Author keywords

Delta and nabla derivatives; Delta and nabla integrals; Time scales

Indexed keywords

EID: 0036853103     PISSN: 10236198     EISSN: None     Source Type: Journal    
DOI: 10.1080/10236190290015272     Document Type: Article

References (15)

1. R.P. Agarwal, M. Bohner, Basic calculus on time scales and some of its applications, Results Math., 35 (1999), 3-22.
2. C.D. Ahlbrandt, M. Bohner, J. Ridenhour, Hamiltonian systems on time scales, J. Math. Anal. Appl., 99 (2000), 561-578.
3. F.M. Atici, G.Sh. Guseinov, On Green's functions and positive solutions for boundary value problems on time scales, J. Comput. Appl. Math., 141(1-2) (2002), 75-99.
4. F.M. Atici, G.Sh. Guseinov, B. Kaymakçalan, On Lyapunov inequality in stability theory for Hill's equation on time scales, J. Inequal. Appl., 5 (2000), 603-620.
5. B. Aulbach, S. Hilger, Linear dynamic processes with inhomogeneous time scale. In: Nonlinear Dynamics and Quantum Dynamical Systems (Gaussig, 1990) Math. Res., Vol. 59, Akademie, Berlin, 1990, pp. 9-20.
6. M. Bohner, J. Castillo, Mimetic methods on measure chains, Computers Math. Appl., 42 (2001), 705-710.
7. M. Bohner, A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhäuser, Boston, 2001.
8. G.Sh. Guseinov, B. Kaymakçalan, On a disconjugacy criterion for second order dynamic equations on time scales, J. Comput. Appl. Math., 141(1-2) (2002), 187-196.
9. E. Fischer, Intermediate Real Analysis, Springer, New York, 1983.
10. S. Hilger, Analysis on measure chains; a unified approach to continuous and discrete calculus, Results Math., 18 (1990), 18-56.
11. S. Hilger, Laplace and Fourier transforms on measure chains, Dynam. Systems Appl., 8 (1999), 471-488.
12. J.W. Kitchen, Calculus of One Variable, Addison-Wesley, California, 1968.
13. V. Lakshmikantham, S. Sivasundaram, B. Kaymakçalan, Dynamic Systems on Measure Chains, Kluwer Academic Publishers, Dordrecht, 1996.
14. K.A. Ross, Elementary Analysis: The Theory of Calculus, Springer, New York, 1990.
15. S. Sailer, Riemann-Stieltjes Integrale auf Zeitmengen, (Schriftliche Hausarbeit, vorgelegt bei: Prof. Dr. B. Aulbach), Universität Augsburg, 1992.