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A cotangent fractional Gronwall inequality with applications
AIMS MathematicsThis article presents the cotangent fractional Gronwall inequality, a novel understanding of the Gronwall inequality within the context of the cotangent fractional derivative. We furnish an explanation of the cotangent fractional derivative and emphasize
Lakhlifa Sadek +3 more
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A stochastic Gronwall inequality in random time horizon and its application to BSDE [PDF]
Journal of Inequalities and Applications, 2020 In this paper, we introduce and prove a stochastic Gronwall inequality in an (unbounded) random time horizon. As an application, we prove a comparison theorem for backward stochastic differential equation (BSDE for short) with random terminal time under ...
Hun O, Mun-Chol Kim, Chol-Kyu Pak
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Journal of Inequalities and Applications, 2019 In this article, we discuss the existence and uniqueness of solution of a delay Caputo q-fractional difference system. Based on the q-fractional Gronwall inequality, we analyze the Ulam–Hyers stability and the Ulam–Hyers–Rassias stability.
Rabia Ilyas Butt +3 more
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A generalized Gronwall inequality and its application to fractional neutral evolution inclusions
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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Journal of Inequalities and Applications, 2023 In this paper, we propose a generalized Gronwall inequality in the context of the ψ -Hilfer proportional fractional derivative. Using Picard’s successive approximation and the definition of Mittag–Leffler functions, we construct the representation ...
W. Sudsutad +4 more
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Journal of Mathematics and Computer Science, 2022 The classical Gronwall inequality is one of the basic tools in the theory of differential and integral equations. In this paper, a new version of this inequality is presented and extended to differential equations with the generalized Hattaf fractional ...
K. Hattaf, A. A. Mohsen, H. Al-Husseiny
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Fractal and Fractional, 2023 Variable-order fractional discrete calculus is a new and unexplored part of calculus that provides extraordinary capabilities for simulating multidisciplinary processes. Recognizing this incredible potential, the scientific community has been researching
Tareq Hamadneh +5 more
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Electronic Journal of Differential Equations, 2021 We study the asymptotic behaviour of global solutions of some nonlinear integral equations related to some Caputo fractional initial value problems. We consider problems of fractional order between 0 and 1 and of order between 1 and 2, each in two cases:
J. Webb
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A Discrete Grönwall Inequality with Applications to Numerical Schemes for Subdiffusion Problems [PDF]
SIAM Journal on Numerical Analysis, 2018 We consider a class of numerical approximations to the Caputo fractional derivative. Our assumptions permit the use of nonuniform time steps, such as is appropriate for accurately resolving the beh...
Hong-lin Liao, W. McLean, Jiwei Zhang
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Finite-time stability of q-fractional damped difference systems with time delay
AIMS Mathematics, 2021 In this paper, we investigate and obtain a new discrete q-fractional version of the Gronwall inequality. As applications, we consider the existence and uniqueness of the solution of q-fractional damped difference systems with time delay.
Jingfeng Wang, Chuanzhi Bai
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