Results 1 to 10 of about 588 (178)
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
doaj +4 more sources
On Some Vector-Valued Inequalities of Gronwall Type [PDF]
Abstract and Applied Analysis, 2014 In this paper we established some vector-valued inequalities of Gronwall type in ordered Banach spaces. Our results can be applied to investigate systems of real-valued Gronwall-type inequalities.
Dah-Chin Luor
doaj +3 more sources
Gronwall’s inequality on discrete fractional calculus
Computers and Mathematics With Applications, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Paul Eloe
exaly +4 more sources
Remark on Gronwall’s inequality
Proceedings of the Indian Academy of Sciences: 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
exaly +3 more sources
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.
Hamid Baghani +2 more
exaly +3 more sources
A class of stochastic Gronwall’s inequality and its application [PDF]
Journal of Inequalities and Applications, 2018 This paper puts forward the basic form of stochastic Gronwall's inequality and uses, respectively, the iterative method, the integral method and the martingale representation method to prove it. Then it presents an application to prove a comparison theorem of L p solutions for one-dimensional backward stochastic differential equations under the ...
Xin Wang, Shengjun Fan
exaly +5 more sources
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.
Thabet Abdeljawad +2 more
exaly +2 more sources
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
doaj +2 more sources
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
doaj +1 more source
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.
openaire +2 more sources