Results 181 to 190 of about 37,785 (206)
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A Generalized Gronwall-Bellman Inequality
Siberian Mathematical Journal, 2020In this paper, some Gronwall-Bellman-type integral inequalities in which the argument of the exponent depends linearly on \(N\). Specifically, the following result is established: Let \(u(x)\), \(A(x)\) be nonnegatine continuous functions on \([0,x_0]\) satisfies \[ u(x) \le A + N\int^{x}_{0}P_m(N(x-\zeta))u(\zeta)d\zeta,\; x\in [0,x_0],\, x_0>0 ...
V. Romanov
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Gronwall type inequality on generalized fractional conformable integral operators
Analysis, 2023In 2015, Abdeljawad defined the conformable fractional derivative (Grunwald–Letnikov technique) to iterate the conformable fractional integral of order 0 < α ≤ 1 ...
Vandana Palsaniya +3 more
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2023 International Conference on Fractional Differentiation and Its Applications (ICFDA), 2023
The dynamics of fractional-order difference neural networks are currently a major research area, with several noteworthy discoveries. The dynamics of discrete-time neural networks with $\hbar$-fractional nonlocal and nonsingular kernels, on the other ...
Amel Hioual +3 more
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The dynamics of fractional-order difference neural networks are currently a major research area, with several noteworthy discoveries. The dynamics of discrete-time neural networks with $\hbar$-fractional nonlocal and nonsingular kernels, on the other ...
Amel Hioual +3 more
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Generalizations of Gronwall-Bellman-Reid inequalities
Applied Mathematics and Computation, 1991In the paper, the authors consider some one-variable linear and nonlinear integral inequalities of the Gronwall-type. Some linear inequalities involving iterated integral functionals are discussed in the first three theorems, which are all special cases of an inequality considered by this reviewer [J. Math. Anal. Appl.
Zaghrout, A. A. S., El-Dawaliby, N.
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Stochastic Analysis and Applications, 2019
In many cases, the existence and uniqueness of the solution of a differential equation are proved using fixed point theory. In this paper, we utilize the theory of operators and ingenious techniques to investigate the well-posedness of mild solution to ...
Xiao-Li Ding, C. Daniel, J. Nieto
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In many cases, the existence and uniqueness of the solution of a differential equation are proved using fixed point theory. In this paper, we utilize the theory of operators and ingenious techniques to investigate the well-posedness of mild solution to ...
Xiao-Li Ding, C. Daniel, J. Nieto
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Sharp generalizations of stochastic Gronwall inequalities
2023In dieser Arbeit betrachten wir zwei stochastische Ungleichungen, welche miteinander zusammenhängen: Eine Ungleichung von Lenglart (1977) und eine Klasse stochastischer Gronwall-Ungleichungen, die von Renesse und Scheutzow (2010), Scheutzow (2013), Xie und Zhang (2020) und Mehri und Scheutzow (2021) studiert wurden.
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Mathematics
In this work, we derive novel theoretical results concerning well-posedness and Ulam–Hyers stability. Specifically, we investigate the well-posedness of Caputo–Katugampola fractional stochastic delay integro-differential equations.
A. M. Djaouti, Muhammad Imran Liaqat
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In this work, we derive novel theoretical results concerning well-posedness and Ulam–Hyers stability. Specifically, we investigate the well-posedness of Caputo–Katugampola fractional stochastic delay integro-differential equations.
A. M. Djaouti, Muhammad Imran Liaqat
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On some nonlinear generalizations of Gronwall’s inequality
Proceedings of the Indian Academy of Sciences - Section A, 1976Some useful nonlinear generalizations of the Gronwall’s inequality which contain, as special cases, the recent generalizations of this inequality given by I. Bihari, D. Willett and J. S. W. Wong and several recent works are presented.
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Some remarks on the Gronwall integral inequality
Mathematical methods in the applied sciences, 2022In this paper, a generalized Volterra‐type integral inequality is developed. On the basis of this inequality, the effect of fractional‐order ω$$ \omega $$ on the application of the integer‐order Gronwall integral inequality (IOGII) is discussed ...
Feifei Du, Jun‐Guo Lu
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