[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.14403/jcms.2016.29.2.255

ON DELTA ALPHA DERIVATIVE ON TIME SCALES

Zhao, Dafang (School of Mathematics and Statistics Hubei Normal University)
You, Xuexiao (School of Mathematics and Statistics Hubei Normal University)
Cheng, Jian (School of Mathematics and Statistics Hubei Normal University)

Publication Information

Journal of the Chungcheong Mathematical Society / v.29, no.2, 2016 , pp. 255-265 More about this Journal

Abstract

In this paper, we define and study the delta alpha derivative on time scales. Many basic properties of delta alpha derivative will be obtained.

Keywords

delta alpha derivative; delta derivative; time scales;

Citations & Related Records

Times Cited By KSCI : 3 (Citation Analysis)

Reference
Cited By KSCI

1	K. Miller and B. Ross, An introduction to the fractional calculus and fractional differential equations, New York: Wiley, 1993.
2	K. B. Oldham and J. Spanier, The fractional calculus, Academic Press, New York and London, 1974.
3	I. Podlubny, Fractional differential equations. Academic Press, San Diego, 1999.
4	J. Sabatier, O. P. Agrawal, and J. A. T. Machado, Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, Springer, 2007.
5	R. Herrmann, Fractional Calculus:An Introduction for Physicists, World Scientific, Singapore, 2014.
6	I. Tejado, D. Valrio, and N. Valrio, Fractional Calculus in Economic Growth Modelling: The Spanish Case, Controlo2014 C Proceedings of the 11th Portuguese Conference on Automatic Control Lecture Notes in Electrical Engineering, 2015, 321, 449-458.
7	R. P. Meilanov and R. A. Magomedov, Thermodynamics in Fractional Calculus, Journal of Engineering Physics and Thermophysics, 87(6) (2014), 1521-1531. DOI
8	A. Carpinteri, P. Cornetti, and A. Sapora, Nonlocal elasticity: an approach based on fractional calculus, Meccanica 49(11) (2014), 2551-2569. DOI
9	R. Khalil, M. Al Horani, A. Yousef, and M. Sababheh, A new definition of fractional derivative, Journal of Computational and Applied Mathematics 264 (2014), 57-66.
10	M. Bohner and A. Peterson, Dynamic equations on time scales. An introduction with applications, Birkhauser, Boston, 2001.
11	M. Bohner and A. Peterson, Advances in Dynamic Equations on Time Scales, Birkhauser, Boston, 2004.
12	S. Hilger, Ein MaBkettenkalkul mit Anwendung auf Zentrumsmannigfaltigkeiten, Ph. D. Thesis, Universtat Wurzburg, 1988.
13	S. Hilger, Analysis on measure chains- A unified approach to continuous and discrete calculus, Results Math. (18) (1990), 18-56. DOI
14	M. Bohner and G. S. Guseinov, The convolution on time scales, Abstr. Appl. Anal. Vol. 2007, Article ID 58373, 24 pages.
15	A. Peterson and B. Thompson, Henstock-Kurzweil Delta and Nabla Integrals,, J. Math. Anal. Appl. 323 (2006), 162-178. DOI
16	X. You and D. Zhao, On convergence theorems for the McShane integral on time scales, J. Chungcheong Math. Soc. 25 (2012), no. 3, 393-400. DOI
17	X. You, Ch. Jian, and D. Zhao, On strong $M_{\alpha}$ integral of Banach-valued functions, J. Chungcheong Math. Soc. 26 (2013), no. 2, 259-268. DOI
18	D. Zhao, X. You, and Ch. Jian, The Riemann-Stieltjes diamond-alpha integral on Time Scales, J. Chungcheong Math. Soc. 28 (2015), no. 1, 53-63. DOI
19	C. Goodrich and A. C. Peterson, Discrete Fractional Calculus, Springer, 2015.