# Explicit bound on some retarded integral inequalities and applications

Volume 4, Issue 1, pp 121-129 Publication Date: 2017-12-17

### Authors

Badreddine Meftah - Laboratoire des t\'{e}l\'{e}communications, Facult\'{e} des Sciences et de la Technologie, University of 8 May 1945 Guelma, P.O. Box 401, 24000 Guelma, Algeria
Abdourazek Souahi - University of Badji Mokhtar Annaba, Algeria.

### Abstract

In this paper, we establish some new retarded integral inequalities, which can be used as tool in the qualitative study of certain properties of retarded integro-differential equations.

### Keywords

retarded inequality, explicit bound, Gronwall-Bellman inequality

### References

• [1] R. Bellman, The stability of solutions of linear differential equations, Duke Math. J.,, 10 (1943), 643–647

• [2] R. Bellman, Asymptotic series for the solutions of linear differential-difference equations, Rend. Circ. Mat. Palermo , 2(7) (1958), 261–269

• [3] H. El-Owaidy, A. Abdeldaim, A.A. El-Deeb, , On some new nonlinear retarded integral inequalities with iterated integrals and their applications in differential-integral equations, , Math. Sci. Lett., 3 (2014), , 3 (2014), 157–164

• [4] Y. H. Kim, On some new integral inequalities for functions in one and two variables, Acta Math. Sin. (Engl. Ser.), 21 (2005), ., 21 (2005), 423–434

• [5] ] O. Lipovan, A retarded Gronwall-like inequality and its applications, J. Math. Anal. Appl., , 252 (2000), 389–401

• [6] T. H. Gronwall, Note on the derivatives with respect to a parameter of the solutions of a system of differential equations, Ann. of Math. (2), 20 (1919), , 20 (1919), 292–296

• [7] B. G. Pachpatte, Explicit bounds on certain integral inequalities, J. Math. Anal. Appl., 267 (2002), . , 267 (2002), 48–61

• [8] M. H. M. Rashidi, Explicit bounds on retarded Gronwall-Bellman inequality, Tamkang , J. Math., 43 (2012), , 43 (2012), 99–108