Further Nonlinear Retarded Integral Inequalities for Gronwall–Bellman Type and Their Applications

Shakoor, Abdul; Ali, Ilyas; Azam, Muhammad; Rehman, Abdur; Iqbal, Muhammad Zahid

doi:10.1007/s40995-019-00745-x

Cited by 5 publications

(3 citation statements)

References 19 publications

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“…Let J(r) be the right hand side of ( 17) that is a non-negative and nondecreasing function on R + , and J(0) = q(0). Thus, from (17) we have…”

Section: Results On Retarded Integral Inequalitiesmentioning

confidence: 99%

“…A huge number of useful generalizations of ( 1) and (3) were given by many mathematicians and scientists after the establishment of Gronwall's inequality and the Gronwall-Bellman inequality which can be found in [4][5][6][10][11][12][13][14][15][16][17][18][19][20]. Among them, Abdeldaim and Yakout [16] in 2011 extended the inequality (3) as given below:…”

Section: Introductionmentioning

confidence: 99%

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New Nonlinear Retarded Integral Inequalities and Their Applications to Nonlinear Retarded Integro-Differential Equations

Samar,

Zhu,

Shakoor

et al. 2024

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The purpose of this article is to present some new nonlinear retarded integral inequalities which can be utilized to study the existence, stability, boundedness, uniqueness, and asymptotic behavior of solutions of nonlinear retarded integro-differential equations, and these inequalities can be used in the symmetrical properties of functions. These inequalities also generalize some former famous inequalities in the literature. Two examples as applications will be provided to demonstrate the strength of our inequalities in estimating the boundedness and global existence of the solution to initial value problems for nonlinear integro-differential equations and differential equations which can be seen in graphs. This research work will ensure opening new opportunities for studying nonlinear dynamic inequalities on a time-scale structure of a varying nature.

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“…Let J(r) be the right hand side of ( 17) that is a non-negative and nondecreasing function on R + , and J(0) = q(0). Thus, from (17) we have…”

Section: Results On Retarded Integral Inequalitiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

New Nonlinear Retarded Integral Inequalities and Their Applications to Nonlinear Retarded Integro-Differential Equations

Samar,

Zhu,

Shakoor

et al. 2024

Axioms

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show abstract

“…Recently, many new results on the nonlinear retarded integral inequalities can be found in [3,7,9,11,14,17] and the references given therein. Theorem 1.1 ([18]).…”

Section: Introductionmentioning

confidence: 99%

A class of nonlinear delay integral inequalities for two-variable functions and their applications in Volterra integral equations

Kriket,

Boudeliou

2023

J. Math. Computer Sci.

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In this paper, we establish some new nonlinear integral inequalities with delay in two independent variables which generalize some known inequalities recently obtained. These results can be used as handy tools to study the boundedness of solutions of Volterra integral equations. An application is given to illustrate how our results can be applied to study the boundedness of the solutions of certain Volterra equations.

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Results for Retarded Nonlinear Integral Inequalities with Mixed Powers and Their Applications to Delay Integrodifferential Equations

Shakoor,

Samar,

Athar

et al. 2023

Ukr Math J

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Further Nonlinear Retarded Integral Inequalities for Gronwall–Bellman Type and Their Applications

Cited by 5 publications

References 19 publications

New Nonlinear Retarded Integral Inequalities and Their Applications to Nonlinear Retarded Integro-Differential Equations

New Nonlinear Retarded Integral Inequalities and Their Applications to Nonlinear Retarded Integro-Differential Equations

A class of nonlinear delay integral inequalities for two-variable functions and their applications in Volterra integral equations

Results for Retarded Nonlinear Integral Inequalities with Mixed Powers and Their Applications to Delay Integrodifferential Equations

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