Results 1 to 10 of about 610,482 (163)
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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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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A discrete fractional Gronwall inequality [PDF]
Proceedings of the American Mathematical Society, 2012 Gronwall type inequalities within the discrete fractional settings are derived and discussed.
R. Ferreira
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The -Fractional Analogue for Gronwall-Type Inequality [PDF]
Journal of Function Spaces and Applications, 2013 We utilize -fractional Caputo initial value problems of order to derive a -analogue for Gronwall-type inequality. Some particular cases are derived where -Mittag-Leffler functions and -exponential type functions are used.
Thabet Abdeljawad, Jehad O. Alzabut
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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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Short proof of a discrete gronwall inequality
Discrete Applied Mathematics, 1987 In the classical discrete Gronwall inequality \(\{x_ n\leq a_ n+\sum^{n-1}_{j=n_ 0}b_ jx_ j,\quad n=n_ 0,...,N\quad implies\quad x_ n\leq a^*\prod^{n-1}_{j=n_ 0}(1+b_ j)\}\) the description of the multiplier \(a^*\) is improved and the use of such inequality in stability considerations for difference equations is illustrated.
D. Clark
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Integral inequalities similar to Gronwall inequality
Electronic Journal of Differential Equations, 2007 In the present paper, we establish some nonlinear integral inequalities for functions of one variable, with a further generalization functions with n independent variables.
Hassane Khellaf, Mohamed Denche
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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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