Bounds of Certain Dynamic Inequalities on Time Scales

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Deepak B. Pachpatte

Abstract

In this paper we study explicit bounds of certain dynamic integral inequalities on time scales. These estimates give the bounds on unknown functions which can be used in studying the qualitative aspects of certain dynamic equations. Using these inequalities we prove the uniqueness of some partial integro-differential equations on time scales.

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References

  1. S. Andras and A. Meszaros, Wendroff Type inequalities on time scales via Picard Operators, Math. Inequal. Appl.,17,1(2013),159-174.
  2. M. Bohner and A. Peterson, Dynamic equations on time scales, Birkhauser Boston/Berlin, (2001).
  3. M. Bohner and A. Peterson, Advances in Dynamic equations on time scales, Birkhauser Boston/Berlin, (2003).
  4. S. Hilger, Analysis on Measure chain-A unified approch to continuous and discrete calculus, Results. Math., 18:18-56, 1990.
  5. W. N. Li, Some Pachpatte type inequalities on time scales, Comput. Math. Appl. Vol. 57, Iss. 2, 2009, P.275-282
  6. L. Li, M. Han, Some new dynamic Opial type inequalities and applications for second order integro-differential dynamic equations on time scales, Appl. Math. Comput.,Vol. 232, 2014, P. 542-547
  7. F. Meng, J. Shao, Some new Volterra Fredholm type dynamic integral inequalities on time scales, Appl. Math. Comput., Vol. 223, 2013, P. 444-451.
  8. D. B. Pachpatte, Explicit estimates on integral inequalities with time scale, J. Inequal. Pure. Appl. Math., Vol. 7, Issue 4, Artivle 143, 2006.
  9. D. B. Pachpatte, Integral Inequalitys for partial dynamic equations on time scales, Electron. J. Differential Equations,Vol. 2012 (2012), No. 50, 1C7.
  10. D. B. Pachpatte, Properties of solutions to nonlinear dynamic integral equations on Time Scales, Electron. J. Differential Equations,Vol. 2008(2008). No. 130. pp.1-8.
  11. S.H. Saker, Applications of Opial inequalities on time scales on dynamic equations with damping terms, Math. Comput. Modelling, Vol. 58, Iss. 11?12, 2013, P.1777-1790
  12. Y. Sun, T. Hassan, Some nonlinear dynamic integral inequalities on time scales, Appl. Math. Comput., Vol 220, 2013, P. 221-225.
  13. A. Tuna, S. Kutukcu, Some integral inequalities on time scales, Appl. Math. Mech. 2008, 29(1):23-29.
  14. L. Yin and F. Qi, Some Integral Inequalities on Time Scales, Results. Math. 64 (2013), 371-381.