Results 41 to 50 of about 610,482 (163)

On approximation of the solutions of delay differential equations by using piecewise constant arguments

International Journal of Mathematics and Mathematical Sciences, 1991
By using the Gronwall Bellman inequality we prove some limit relations between the solutions of delay differential equations with continuous arguments and the solutions of some related delay differential equations with piecewise constant arguments(EPCA).
Istevan Györi
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Gronwall’s inequality on discrete fractional calculus

Computers & Mathematics with Applications, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Atici, Ferhan M., Eloe, Paul W.
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A generalized q-fractional Gronwall inequality and its applications to nonlinear delay q-fractional difference systems

Journal of Inequalities and Applications, 2016
In this paper, we state and prove a new discrete q-fractional version of the Gronwall inequality. Based on this result, a particular version expressed by means of the q-Mittag-Leffler function is provided.
T. Abdeljawad, J. Alzabut, D. Baleanu
semanticscholar   +2 more sources

Lebesgue-p Norm Convergence Analysis of PDα-Type Iterative Learning Control for Fractional-Order Nonlinear Systems

Discrete Dynamics in Nature and Society, 2018
The first-order and second-order PDα-type iterative learning control (ILC) schemes are considered for a class of Caputo-type fractional-order nonlinear systems.
Lei Li
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A New Gronwall–Bellman Inequality in Frame of Generalized Proportional Fractional Derivative

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, Weerawat Sudsutad, Zeynep Kayar, Hamid Baghani   +3 more
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Controllability results of neutral Caputo fractional functional differential equations

AIMS Mathematics, 2023
In this paper, using the properties of the phase space on infinite delay, generalized Gronwall inequality and fixed point theorems, the existence and controllability results of neutral fractional functional differential equations with multi-term Caputo ...
Qi Wang, Chenxi Xie, Qianqian Deng, Yuting Hu   +3 more
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Remark on Gronwall’s inequality

Proceedings Mathematical Sciences, 1992
The present note is devoted to abstract analogues of the Gronwall inequality in classical propositional calculus. Let \(a_ 1,a_ 2,\dots,b_ 1,b_ 2,\dots,\) and \(x_ 1,x_ 2,\dots\) be infinite sets of statement variables and \(\sim\), \(\land\), \(\lor\), \(\supset\), and \(\equiv\) connectives in classical propositional calculus. The main results of the
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A Linear Generalization of Gronwall's Inequality [PDF]

Proceedings of the American Mathematical Society, 1965
where k(t, s) and w0(t) are known non-negative functions and u(t) is an unknown non-negative function. For examples, one can refer to Bellman [l, pp. 35 ff.], Coddington and Levinson [2, pp. 37 ff.], Willett [3], and others. In order to obtain from (1.1) a genuine upper bound for u(t), i.e., an upper bound independent of u, it seems necessary to ...
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On the generalized coupled Hadamard-Gronwall-Bellman-type inequalities with applications to fractional delay systems

AIMS Mathematics
The Gronwall-Bellman inequality is a primary tool for proving various types of stability. For this importance, the present paper focuses on the generalized forms of the well-known Gronwall-Bellman inequality in the context of the Hadamard fractional ...
Sina Etemad, Ali Akgül, J. Alberto Conejero   +2 more
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Bounds for Tur\'anians of modified Bessel functions

, 2013
Motivated by some applications in applied mathematics, biology, chemistry, physics and engineering sciences, new tight Tur\'an type inequalities for modified Bessel functions of the first and second kind are deduced.
Alexandrov, Amos, Baricz, Baricz, Baricz, Baricz, Baricz, Baricz, Baricz, Baricz, Baricz, Bertini, Bhattacharya, Erdélyi, Fabrizi, Giorgi, Giorgi, Grandison, Gronwall, Hamsici, Hamsici, Hamsici, Hartman, Hartman, Hartman, Hasan, Ismail, Ismail, Ismail, Joshi, Klimek, Kokologiannaki, Laforgia, Laforgia, Lechleiter, Lombardo, Lorch, Lushnikov, Marchand, Marchand, Marchand, Nasell, Paltsev, Penfold, Phillips, Radwan, Radwan, Robert, Schlenk, Segura, Simitev, Simon, Tanabe, Thabane, Thiruvenkatachar, van Haeringen, Watson, Watson, Árpád Baricz   +58 more
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