Results 11 to 20 of about 610,482 (163)
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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The Gronwall inequality for modified Stieltjes integrals [PDF]
Proceedings of the American Mathematical Society, 1968 Schmaedeke, W. W., Sell, G. R.
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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 Gronwall inequality for linear Stieltjes integrals [PDF]
Proceedings of the American Mathematical Society, 1969 J. Herod
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Linear generalizations of Gronwall’s inequality [PDF]
Proceedings of the American Mathematical Society, 1976 A variety of linear generalizations of Gronwall's inequality, including recent multivariable results of D. R. Snow and E. C. Young, are subsumed and extended by simple arguments involving the resolvent kernel of the integral operator.
Chandra, Jagdish, Davis, Paul W.
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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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A Gronwall inequality and the Cauchy-type problem by means of ψ-Hilfer operator [PDF]
Differential Equations & Applications, 2017 In this paper, we propose a generalized Gronwall inequality through the fractional integral with respect to another function. The Cauchy-type problem for a nonlinear differential equation involving the $\psi$-Hilfer fractional derivative and the ...
J. Sousa, E. C. Oliveira
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, 2021 The main intention of the present research study is focused on the analysis of a Caputo fractional integro-differential boundary problem (CFBVP) in which the right-hand side of supposed differential equation is represented as a sum of two nonlinear terms.
S. Rezapour +4 more
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