New retarded nonlinear integral inequalities of Gronwall-Bellman-Pachpatte type and their applications

• Autorzy: Kale Nagesh

Identyfikatory

DOI

10.1515/jaa-2023-0122

• Języki publikacji: EN

Abstrakty

EN

The goal of the present article is to offer several new retarded nonlinear inequalities of Gronwall, Bellman, and Pachpatte kind for a class of integral and integro-differential equations. These inequalities generalize and provide new formulations of some well-known results in the mathematical framework of integral and differential inequalities that have been derived currently as well as in earlier times. These results can be utilized to investigate diverse aspects, both qualitative and quantitative, of a class of aforementioned equations. We propose a few applications to ensure the effectiveness of these inequalities.

Słowa kluczowe

EN

integral inequality; retarded integral equations; Gronwall-Bellman-Pachpatte type

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2024
• Tom: Vol. 30, nr 2
• Strony: 379--391
• Opis fizyczny: Bibliogr. 20 poz., 1 wykr.

Twórcy

autor

Kale Nagesh

• Department of Mathematics, Sant Rawool Maharaj Mahavidyalaya Kudal, Sindhudurga-416520, India

• https://orcid.org/0000-0002-7669-3507

Bibliografia

• [1] A. Abdeldaim and A. A. El-Deeb, On generalized of certain retarded nonlinear integral inequalities and its applications in retarded integro-differential equations, Appl. Math. Comput. 256 (2015), 375-380.
• [2] A. Abdeldaim and M. Yakout, On some new integral inequalities of Gronwall-Bellman-Pachpatte type, Appl. Math. Comput. 217 (2011), no. 20, 7887-7899.
• [3] R. P. Agarwal, S. Deng and W. Zhang, Generalization of a retarded Gronwall-like inequality and its applications, Appl. Math. Comput. 165 (2005), no. 3, 599-612.
• [4] D. Baĭnov and P. Simeonov, Integral Inequalities and Applications, Math. Appl. 57, Kluwer Academic, Dordrecht, 1992.
• [5] 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), no. 4, 292-296.
• [6] S. Kendre and N. Kale, On some new nonlinear Volterra-Fredholm type discrete inequalities and its applications, J. Math. Inequal. 14 (2020), no. 2, 437-453.
• [7] S. Kendre and N. Kale, On nonlinear Volterra-Fredholm type discrete fractional sum inequalities, Fract. Differ. Calc. 11 (2021), no. 1, 17-33.
• [8] S. D. Kendre and N. R. Kale, Some generalizations of linear finite difference inequalities of Pachpatte type, Asian-Eur. J. Math. 14 (2021), no. 3, Article ID 2150038.
• [9] O. Lipovan, A retarded Gronwall-like inequality and its applications, J. Math. Anal. Appl. 252 (2000), no. 1, 389-401.
• [10] B. G. Pachpatte, A note on Gronwall-Bellman inequality, J. Math. Anal. Appl. 44 (1973), 758-762.
• [11] B. G. Pachpatte, Inequalities for Differential and Integral Equations, Math. Sci. Eng. 197, Academic Press, San Diego, 1998.
• [12] B. G. Pachpatte, Integral and Finite Difference Inequalities and Applications, North-Holland Math. Stud. 205, Elsevier Science, Amsterdam, 2006.
• [13] A. Shakoor, I. Ali, M. Azam, A. Rehman and M. Zahid Iqbal, Further nonlinear retarded integral inequalities for Gronwall-Bellman type and their applications, Iran. J. Sci. Technol. Trans. A Sci. 43 (2019), no. 5, 2559-2568.
• [14] A. Shakoor, I. Ali, S. Wali and A. Rehman, Some generalizations of retarded nonlinear integral inequalities and its applications, J. Math. Inequal. 14 (2020), no. 4, 1223-1235.
• [15] A. Shakoor, M. Samar, T. Athar and M. Saddique, Results for retarded nonlinear integral inequalities with mixed powers and their applications to delay integrodifferential equations, Ukrainian Math. J. 75 (2023), no. 3, 478-493.
• [16] A. Shakoor, M. Samar, S. Wali and M. Saleem, Retarded nonlinear integral inequalities of Gronwall-Bellman-Pachpatte type and their applications, Honam Math. J. 45 (2023), no. 1, 54-70.
• [17] H. Song and M. Feng, Some generalizations of delay integral inequalities of Gronwall-Bellman type with power and their applications, Math. Found. Comput. 5 (2022), 45-55.
• [18] Y. Tian and M. Fan, Nonlinear integral inequality with power and its application in delay integro-differential equations, Adv. Difference Equ. 2020 (2020), Paper No. 142.
• [19] W.-S. Wang, Some retarded nonlinear integral inequalities and their applications in retarded differential equations, J. Inequal. Appl. 2012 (2012), Paper No. 75.
• [20] C. Zhao, Some integral inequalities for differential equations, J. Binzhou Teachers College 17 (2001), 41-46.