On Some New Retarded Nonlinear Integral Inequalities and Their Applications

El-Owaidy, H. M.; Abdeldaim, A.; El‐Deeb, Ahmed A.

doi:10.12785/msl/030304

Cited by 22 publications

(13 citation statements)

References 18 publications

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“…During the past few years, some investigators have established a lot of useful and interesting integral inequalities in order to achieve various goals; see [3][4][5][6][7][8][9][10] and the references cited therein. In this paper, on the basis of [3,4,5], we discuss a class of nonlinear weakly singular integral inequality…”

Section: T T S U T U G S U S Q S Ds G S U S U S H U D Dsmentioning

confidence: 99%

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Estimation of Unknown Function of a Class of Nonlinear Integral Inequality

Yun¹,

Wang²

2015

Proceedings of the 2015 International Conference on Education, Management, Information and Medicine

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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.

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Section: T T S U T U G S U S Q S Ds G S U S U S H U D Dsmentioning

confidence: 99%

“…In this paper, on the basis of [3,4,5], we discuss a class of nonlinear weakly singular integral inequality…”

Section: T T S U T U G S U S Q S Ds G S U S U S H U D Dsmentioning

confidence: 99%

See 1 more Smart Citation

Estimation of Unknown Function of a Class of Nonlinear Integral Inequality

Yun¹,

Wang²

2015

Proceedings of the 2015 International Conference on Education, Management, Information and Medicine

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“…In 2008, Ma and Pecaric [1] With the development of the theory of differential equations, integral inequalities have been paid much attention by many authors. We refer to the papers [3][4][5][6][7][8][9][10] and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%

Estimation of Unknown Function of a Class of Nonlinear Weakly Singular Integral Inequality

Huang¹,

Wang²

2015

Proceedings of the 2015 International Conference on Advanced Manufacturing and Industrial Application

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Abstract-In this paper, we investigate a nonlinear weakly singular integral inequality. The upper bounds of the embedded unknown functions are estimated explicitly by the definitions and rules of conformable fractional differential and conformable fractional integration, the techniques of change of variable, and the method of amplification. The derived results can be applied in the study of qualitative properties of solutions of conformable fractional integral equations.

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“…In 2014, El-Owaidy, Abdeldaim, and El-Deeb [4] discussed a new nonlinear integral inequality with a nonconstant term outside the integrals…”

Section: Introductionmentioning

confidence: 99%

Estimation of Unknown Function of a Class of Integral Inequalities with pth Power

Lu¹,

Wang²,

Zhong³

2015

Proceedings of the 2015 International Conference on Education, Management, Information and Medicine

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Abstract. Fractional differential equations and fractional integral equations have gained considerable importance and attention due to their applications in many engineering and scientific disciplines. Gronwall-Bellman inequalities are important tools in the study of existence, uniqueness, boundedness, stability and other qualitative properties of solutions of Fractional differential equations and fractional integral equations. In this paper, we discuss a class of integral inequalities with pth power, which includes a nonconstant term outside the integrals. Using the definitions and properties of modified Riemann-Liouville fractional derivative and Riemann-Liouville fractional integral, the upper bounds of the unknown function is estimated explicitly. The derived result can be applied in the study of qualitative properties of solutions of fractional integral equations.

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On Some New Retarded Nonlinear Integral Inequalities and Their Applications

Cited by 22 publications

References 18 publications

Estimation of Unknown Function of a Class of Nonlinear Integral Inequality

Estimation of Unknown Function of a Class of Nonlinear Integral Inequality

Estimation of Unknown Function of a Class of Nonlinear Weakly Singular Integral Inequality

Estimation of Unknown Function of a Class of Integral Inequalities with pth Power

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