Some Gamidov like integral inequalities on time scales and applications

Published in Issue 2025-11-09

How to Cite

Some Gamidov like integral inequalities on time scales and applications. (2025). Communications in Nonlinear Analysis, 3(1). https://oiccpress.com/cna/article/view/17894

PDF views: 282

Abstract

In the present paper, we establish some Gamidov like integral inequalities on time scales, the obtainedresults can be used as tools for the study of certain qualitative properties of solutions for differential anddifference equations.

Keywords

  • Dynamic equations,
  • time scale,
  • integral inequality

References

  1. [1] A. Abdeldaim, M. Yakout, On some new integral inequalities of Gronwall-Bellman-Pachpatte type, Appl. Math. Comput.,217 (2011), 7887-7899.
  2. [2] R. Agarwal, M. Bohner, A. Peterson, Inequalities on time scales: a survey, Math. Inequal. Appl., 4 (2001), 535-557.
  3. [3] D. R. Anderson, Time-scale integral inequalities. JIPAM. J. Inequal. Pure Appl. Math. 6 (2005), 15 pages.
  4. [4] D. Bainov, P. Simeonov, Integral inequalities and applications, Kluwer Academic Publishers Group, Dordrecht, (1992).
  5. [5] P. R. Beesack, Gronwall inequalities, Carleton University, Ottawa, (1975).
  6. [6] M. Bohner, A. Peterson, Dynamic equations on time scales. An introduction with applications, Birkhauser Boston, Inc., Boston, MA, (2001).
  7. [7] K. Cheng, C. Guo, M. Tang, Some nonlinear Gronwall-Bellman-Gamidov integral inequalities and their weakly singularanalogues with applications, Abstr. Appl. Anal., 2014 (2014), 9 pages.
  8. [8] H. El-Owaidy, A. Ragab, A. Abdeldaim, On some new integral inequalities of Growall-Bellman [Gronwall-Bellman] type,Appl. Math. Comput., 106 (1999), 289-303.
  9. [9] J. Gu, F. Meng, Some new nonlinear Volterra-Fredholm type dynamic integral inequalities on time scales, Appl. Math.Comput., 245 (2014), 235-242.
  10. [10] S. Hilger, Analysis on measure chains|a unied approach to continuous and discrete calculus, Results Math., 18 (1990),18-56.
  11. [11] Y. Huang, W.-S. Wang, Y. Huang, A class of Volterra-Fredholm type weakly singular difference inequalities with powerfunctions and their applications, J. Appl. Math., 2014 (2014), 9 pages.
  12. [12] F. Jiang, F. Meng, Explicit bounds on some new nonlinear integral inequalities with delay, J. Comput. Appl. Math., 205(2007), 479-486.
  13. [13] W. N. Li, Some new dynamic inequalities on time scales, J. Math. Anal. Appl., 319 (2006), 802-814.
  14. [14] O. Lipovan, A retarded Gronwall-like inequality, and its applications, J. Math. Anal. Appl. 252 (2000), 389-401.
  15. [15] F. W. Meng, W. N. Li, On some new integral inequalities and their applications, Appl. Math. Comput., 148 (2004),381-392.
  16. [16] F. Meng, J. Shao, Some new Volterra-Fredholm type dynamic integral inequalities on time scales, Appl. Math. Comput., 223 (2013), 444-451.
  17. [17] B. G. Pachpatte, Inequalities for differential and integral equations, Mathematics in Science and Engineering, 197. Academic Press, Inc., San Diego, CA, (1998).
  18. [18] B. G. Pachpatte, Explicit bounds on Gamidov type integral inequalities, Tamkang J. Math., 37 (2006), 1-9.
  19. [19] D. B. Pachpatte, Estimates of certain integral inequalities on time scales, J. Math., 2013 (2013), 5 pages.
  20. [20] Y. Tian, Y. Cai, L. Li and T. Li, Some dynamic integral inequalities with mixed nonlinearities on time scales, J. Inequal.Appl., 2015 (2015), 10 pages.
  21. [21] Y. Tian, M. Fan, Y. Sun, Certain nonlinear integral inequalities and their applications, Discrete Dyn. Nat. Soc., 2017(2017), 8 pages.