ON BIVARIATE RETARDED INTEGRAL INEQUALITIES AND THEIR APPLICATIONS
Abstract
In this paper, we obtain some retarded integral inequalities in two independent variables which can be used as tools in the theory of partial differential and integral equations with time delays. The presented inequalities are of new forms compared with the existing ones so far in the literature. In order to illustrate the validity of the theorems we give one application for them for the solution to certain fractional order differential equations.
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D. Bainov and P. Simeonov: Integral Inequalities and Applications. Kluwer Academic Publishers, Dordrecht, 1992.
R. Bellman: The stability of solutions of linear differential equations. Duke Math. J., 10 (1943), 643–647.
I. Bihari: generalization of a lemma of Bellman and its application to uniqueness problems of differential equations. Acta. Math. Acad. Sci. Hungar., 7 (1965), 81–94.
T. H. Gronwall: Note on the derivatives with respect to a parameter of the solutions of a system of differential equations. Ann. Math., 20 (1919), 292–296.
O. Lipovan: A retarded Gronwall-like inequality and its applications. J. Math. Anal. Appl., 252 (2000), 389–401.
B. G. Pachpatte: Inequalities for Differential and Integral Equations. Academic Press, New York, 1998.
B. G. Pachpatte: On some new inequalities related to certain inequalities in the theory of differential equations. J. Math. Anal. Appl. 189 (1995) 128–144.
B. G. Pachpatte: On some retarded integral inequalities and applications. J. Inequal. Pure Appl. Math., 3(2), Article 18, 2002.
F. Usta and M. Z. Sarıkaya: Explicit bounds on certain integral inequalities via conformable fractional calculus. Cogent Mathematics, 4: 1277505, 2017.
F. Usta and M. Z. Sarıkaya: Some improvements of conformable fractional integral inequalities. International Journal of Analysis and Applications, 14(2), (2017), 162–166.
F. Usta and M. Z. Sarıkaya: On generalization of pachpatte type inequalities for conformable fractional integral. TWMS J. App. Eng. Math. 8(1), 2018, pp. 106-113.
F. Usta and M. Z. Sarıkaya: on generalization conformable fractional integral inequalities. FILOMAT. (In press).
DOI: https://doi.org/10.22190/FUMI1903553U
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