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• W780977195 abstract "In this paper, we establish a class of iterated integral inequality, which includes a noncons -tant term outside the integrals. The upper bound of the embedded unknown function in the inequality is estimated explicitly by adopting novel analytical techniques, such as: change of variable, amplification method, differential and integration. The derived result can be applied in the study of qualitative properties of solutions of fractional integral equations. Introduction Gronwall-Bellman inequality [1, 2] can be stated as follows: If u and f are non-negative continuous functions on an interval [ , ] a b satisfying ( ) ( ) ( ) , [ , ]. t a u t c f s u s ds t a b     (1) For some constant 0 c  , then ( ) exp( ( ) ), [ , ]. t a u t c f s ds t a b    In 2011, Abdeldaim et al. [3] studied a new integral inequality of Gronwall-Bellman-Pachpatte type 0 0 0 0 ( ) [ ( ) ( ) ( )] ( ) ( )[ ( ) ( ) ( ) ] . t t s u t u g s u s q s ds g s u s u s h u d ds            (2) In 2014, El-Owaidy, Abdeldaim, and El-Deeb[4] investigated a new retarded nonlinear integral inequality ( ) ( ) ( ) ( ) ( ) ( ) ( ) . t t p p a a u t f t g s u s ds h s u s ds       (3) In 2014, Zheng [5] discussed the inequality of the following form" @default.
• W780977195 created "2016-06-24" @default.
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• W780977195 date "2015-01-01" @default.
• W780977195 modified "2023-09-26" @default.
• W780977195 title "Estimation of Unknown Function of a Class of Nonlinear Integral Inequality" @default.
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• W780977195 doi "https://doi.org/10.2991/emim-15.2015.251" @default.
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