A generalized Gronwall inequality and its application to fractional neutral evolution inclusions [PDF]
Journal of Inequalities and Applications, 2016 This paper deals with the fractional neutral evolution differential inclusions. The existence results are established by using the fractional power of operators and a fixed point theorem for multivalued map.
Zufeng Zhang, Zhangzhi Wei
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A more generalized Gronwall-like integral inequality with applications [PDF]
International Journal of Mathematics and Mathematical Sciences, 2003 This paper deals with a new Gronwall-like integral inequality which is a generalization of integral inequalities proved by Engler (1989) and Pachpatte (1992).
Qinghua Ma, Lokenath Debnath
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A Gronwall inequality via the generalized proportional fractional derivative with applications [PDF]
Journal of Inequalities and Applications, 2019 In this paper, we provide a new version for the Gronwall inequality in the frame of the generalized proportional fractional derivative. Prior to the main results, we introduce the generalized proportional fractional derivative and expose some of its ...
Jehad Alzabut +3 more
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A New Gronwall–Bellman Inequality in Frame of Generalized Proportional Fractional Derivative [PDF]
Mathematics, 2019 New versions of a Gronwall−Bellman inequality in the frame of the generalized (Riemann−Liouville and Caputo) proportional fractional derivative are provided.
Jehad Alzabut +3 more
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Ulam stability and data dependence for fractional differential equations with Caputo derivative [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2011 In this paper, Ulam stability and data dependence for fractional differential equations with Caputo fractional derivative of order $\alpha$ are studied. We present four types of Ulam stability results for the fractional differential equation in the case ...
JinRong Wang, Linli Lv, Yong Zhou
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Some generalized Gronwall-Bellman type difference inequalities and applications [PDF]
Journal of Mathematical Inequalities, 2021 . We establish some generalized sums-difference inequalities involving a fi nite sum, which includes three sums and seven sums, respectively. We present the estimation of the inequality is decided by a fi nite recursion.
Zizun Li
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A Generalized Gronwall Inequality for Caputo Fractional Dynamic Delta Operator [PDF]
Progress in Fractional Differentiation and Applications, 2019 In this paper we obtain generalized Gronwall type inequality using Caputo Fractional delta operator. Also we have obtained the existence of solution of Cauchy's Type problem on fractional dynamic equations using dynamic delta operator.
D. Pachpatte
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AIMS Mathematics, 2022 In this paper, a Gronwall inequality involving $ \psi $-fractional integral operator is obtained as a generalization of [23]. An example is listed to show the applications.
Qi Wang, Shumin Zhu
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A Gronwall inequality for a general Caputo fractional operator [PDF]
Mathematical Inequalities & Applications, 2017 In this paper we present a new type of fractional operator, which is a generalization of the Caputo and Caputo--Hadamard fractional derivative operators.
R. Almeida
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Finite-Time Stability of Neutral Fractional Time-Delay Systems via Generalized Gronwalls Inequality [PDF]
Abstract and Applied Analysis, 2014 This paper studies the finite-time stability of neutral fractional time-delay systems. With the generalized Gronwall inequality, sufficient conditions of the finite-time stability are obtained for the particular class of neutral fractional time-delay ...
Pang Denghao, Jiang Wei
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