• 충청수학회지
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• 제31권1호
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• pp.161-166
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• 2018

This paper deals an impulsive fractional integral inequality with singular kernel which can be used in getting the explicit estimate of solutions of impulsive fractional differential equations.

• Journal of applied mathematics & informatics
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• 제34권3_4호
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• pp.193-206
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• 2016

In this paper, we study boundary value problems for fractional integrodifferential equations involving Caputo derivative in Banach spaces. A generalized singular type Gronwall inequality is given to obtain an important priori bounds. Some sufficient conditions for the existence solutions are established by virtue of fractional calculus and fixed point method under some mild conditions.

• Journal of applied mathematics & informatics
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• 제26권5_6호
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• pp.877-888
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• 2008

This paper deals with some new nonlinear delay and weakly singular integral inequalities of Gronwall-Bellman type. These results generalize the inequalities discussed by Xiang and Kuang [19]. Several other inequalities proved by $Medve{\check{d}}$ [15] and Ou-Iang [17] follow as special cases of this paper. This work can be used in the analysis of various problems in the theory of certain classes of differential equations, integral equations and evolution equations. A modification of the Ou-Iang type inequality with delay is also treated in this paper.

• Nonlinear Functional Analysis and Applications
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• 제29권2호
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• pp.545-558
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• 2024

In this study, a class of nonlinear boundary fractional Caputo Volterra-Fredholm integro-differential equations (CV-FIDEs) is taken into account. Under specific assumptions about the available data, we firstly demonstrate the existence and uniqueness features of the solution. The Gronwall's inequality, a adequate singular Hölder's inequality, and the fixed point theorem using an a priori estimate procedure. Finally, a case study is provided to highlight the findings.