Results 61 to 70 of about 3,827,469 (279)
Impulsive stochastic fractional differential equations driven by fractional Brownian motion
Advances in Difference Equations, 2020 In this research, we study the existence and uniqueness results for a new class of stochastic fractional differential equations with impulses driven by a standard Brownian motion and an independent fractional Brownian motion with Hurst index 1 ...
Mahmoud Abouagwa, Feifei Cheng, Ji Li
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Equivalences of Nonlinear Higher Order Fractional Differential Equations With Integral Equations
Mathematical Methods in the Applied Sciences, Volume 48, Issue 6, Page 6930-6942, April 2025.ABSTRACT Equivalences of initial value problems (IVPs) of both nonlinear higher order (Riemann–Liouville type) fractional differential equations (FDEs) and Caputo FDEs with the corresponding integral equations are studied in this paper. It is proved that the nonlinearities in the FDEs can be L1$$ {L}^1 $$‐Carathéodory with suitable conditions.
Kunquan Lan
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Oscillation of generalized differences of H\"older and Zygmund functions
, 2016 In this paper we analyze the oscillation of functions having derivatives in the H\"older or Zygmund class in terms of generalized differences and prove that its growth is governed by a version of the classical Kolmogorov's Law of the Iterated Logarithm ...
Castro, Alejandro J. +2 more
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On the Mean‐Field Limit of Consensus‐Based Methods
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT Consensus‐based optimization (CBO) employs a swarm of particles evolving as a system of stochastic differential equations (SDEs). Recently, it has been adapted to yield a derivative free sampling method referred to as consensus‐based sampling (CBS). In this paper, we investigate the “mean‐field limit” of a class of consensus methods, including
Marvin Koß, Simon Weissmann, Jakob Zech
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Bi-Lipschitz Pieces between Manifolds [PDF]
, 2013 A well-known class of questions asks the following: If $X$ and $Y$ are metric measure spaces and $f:X\rightarrow Y$ is a Lipschitz mapping whose image has positive measure, then must $f$ have large pieces on which it is bi-Lipschitz?
David, Guy C.
core
On Generalized Lipschitz Classes and Fourier Series
Zeitschrift für Analysis und ihre Anwendungen, 2004 In 1967 R. P. Boas Jr. found necessary and sufficient conditions of belonging of a function to a Lipschitz class. Later Boas's findings were generalized by many authors (e.g. M. and S. Izumi (1969), L.-Y. Chan (1991) and others). Recently, L. Leindler (2000) and J. Nemeth (2001) have published two papers, in which they have generalized all the previous
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Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT We study eigenvalue problems for the de Rham complex on varying three‐dimensional domains. Our analysis includes the Helmholtz equation as well as the Maxwell system with mixed boundary conditions and non‐constant coefficients. We provide Hadamard‐type formulas for the shape derivatives under weak regularity assumptions on the domain and its ...
Pier Domenico Lamberti +2 more
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Numerical Study of Random Periodic Lipschitz Shadowing of Stochastic Differential Equations
Discrete Dynamics in Nature and Society, 2018 This paper is devoted to a new numerical approach for the possibility of (ω,Lδ)-periodic Lipschitz shadowing of a class of stochastic differential equations. The existence of (ω,Lδ)-periodic Lipschitz shadowing orbits and expression of shadowing distance
Qingyi Zhan, Xiangdong Xie
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Lipschitz extensions into Jet space Carnot groups [PDF]
, 2009 The aim of this article is to prove a Lipschitz extension theorem for partially defined Lipschitz maps to jet spaces endowed with a left-invariant sub-Riemannian Carnot-Carath\'eodory distance.
Wenger, Stefan, Young, Robert
core
From Stability to Chaos: A Complete Classification of the Damped Klein‐Gordon Dynamics
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT We investigate the transition between stability and chaos in the damped Klein‐Gordon equation, a fundamental model for wave propagation and energy dissipation. Using semigroup methods and spectral criteria, we derive explicit thresholds that determine when the system exhibits asymptotic stability and when it displays strong chaotic dynamics ...
Carlos Lizama +2 more
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