DOI QR코드

DOI QR Code

ON RIEMANN DELTA-ALPHA FRACTIONAL INTEGRALS ON TIME SCALES

  • Zhao, Dafang (School of Mathematics and Statistics, Hubei Normal University) ;
  • Cheng, Jian (School of Mathematics and Statistics, Hubei Normal University)
  • Received : 2015.07.29
  • Accepted : 2016.02.12
  • Published : 2016.03.25

Abstract

In this paper, we introduce and investigate the concept of Riemann Delta-alpha fractional integral on time scales. Many properties of this integral will be obtained.

Keywords

Acknowledgement

Supported by : Educational Commission of Hubei Province of China

References

  1. M. Bohner, A. Peterson, Dynamic equations on time scales. An introduction with applications, Birkhauser, Boston, MA, 2001.
  2. M. Bohner, A. Peterson, Advances in Dynamic Equations on Time Scales, Birkhauser,Boston, 2004.
  3. A. Carpinteri, P. Cornetti, Alberto Sapora, Nonlocal elasticity: an approach based on fractional calculus, Meccanica, (2014),49(11):2551-2569. https://doi.org/10.1007/s11012-014-0044-5
  4. R. Herrmann, Fractional Calculus:An Introduction for Physicists, World Scientific, Singapore, 2014.
  5. S. Hilger, Analysis on measure chains-A unified approach to continuous and discrete calculus, Results Math.,(1990),18:18-56. https://doi.org/10.1007/BF03323153
  6. R. Khalil, M. Al Horani,A. Yousef, M. Sababheh, A new definition of fractional derivative, J. Comput. Appl. Math.,, (2014), 264:57-66.
  7. K. Miller,B. Ross,An introduction to the fractional calculus and fractional differential equations, New York: Wiley,1993.
  8. R. P. Meilanov, R. A. Magomedov, Thermodynamics in Fractional Calculus, J. Eng. Phys. Thermophys.,, (2014),87(6):1521-1531. https://doi.org/10.1007/s10891-014-1158-2
  9. K. B. Oldham,J. Spanier, The fractional calculus, Academic Press, New York and London, 1974.
  10. I. Podlubny, Fractional differential equations, Academic Press, San Diego, 1999.
  11. J. Sabatier, O. P. Agrawal, J. A. T. Machado, Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, Springer, Dordrecht, The Netherlands, 2007.
  12. I. Tejado, D. Valrio, N. Valrio, Fractional Calculus in Economic Growth Modelling:The Spanish Case, Controlo2014 -Proceedings of the 11th Portuguese Conference on Automatic Control Lecture Notes in Electrical Engineering,(2015),321:449-458.