Results 61 to 70 of about 485,864 (198)
A new proof of Gronwall inequality with Atangana- Baleanu fractional derivatives
, 2020 In this study, we establish a new version of Gronwall type integral inequality, which generalizes some previous ones.
Mısır, Adil +2 more
core +1 more source
Traveling Fronts for (q,r)$(q, r)$‐Relativistic Operators: Existence and Asymptotic Properties
Mathematische Nachrichten, Volume 299, Issue 11, Page 3665-3688, November 2026.ABSTRACT A new reaction–diffusion model governed by a (q,r)$(q, r)$‐relativistic type diffusion, generalizing the p$p$‐relativistic one and encompassing singular and/or degenerate diffusivity, is introduced. In the monostable case, some existence results for (decreasing) fronts are then provided, exploiting the study of a suitable two‐point problem ...
Pavel Drábek +2 more
wiley +1 more source
Stochastic Gradient Descent in High Dimensions for Multi‐Spiked Tensor PCA
Communications on Pure and Applied Mathematics, Volume 79, Issue 10, Page 2291-2369, October 2026.ABSTRACT We study the high‐dimensional dynamics of online stochastic gradient descent (SGD) for the multi‐spiked tensor model. This multi‐index model arises from the tensor principal component analysis (PCA) problem with multiple spikes, where the goal is to estimate the unknown signal vectors within the N$N$‐dimensional unit sphere through maximum ...
Gérard Ben Arous +2 more
wiley +1 more source
T(w)o Patch or Not T(w)o Patch: A Novel Biocontrol Model
Mathematical Methods in the Applied Sciences, Volume 49, Issue 13, Page 14697-14743, 15 September 2026.ABSTRACT A number of top‐down biocontrol models have been proposed where the introduced predators' efficacy is enhanced via the provision of additional food (AF). However, if the predator has a pest‐dependent monotone functional response, pest extinction is unattainable. In the current manuscript, we propose a model where a predator with pest‐dependent
Urvashi Verma +2 more
wiley +1 more source
Short proof of a discrete gronwall inequality
Discrete Applied Mathematics, 1987 In the classical discrete Gronwall inequality \(\{x_ n\leq a_ n+\sum^{n-1}_{j=n_ 0}b_ jx_ j,\quad n=n_ 0,...,N\quad implies\quad x_ n\leq a^*\prod^{n-1}_{j=n_ 0}(1+b_ j)\}\) the description of the multiplier \(a^*\) is improved and the use of such inequality in stability considerations for difference equations is illustrated.
openaire +1 more source
Rothe Time Discretization and Weak Solutions for a Cutoff Westervelt System
Numerical Methods for Partial Differential Equations, Volume 42, Issue 5, September 2026.ABSTRACTWe study a fully implicit Rothe time discretization for a cutoff first‐order formulation of the Westervelt equation. The key ingredients are the enthalpy variable and the primitive mobility variable, which turn each nonlinear time step into a uniformly monotone elliptic problem and avoid higher‐order energy estimates and inverse inequalities ...
Marvin Fritz
wiley +1 more source
Numerical Methods for Partial Differential Equations, Volume 42, Issue 5, September 2026.ABSTRACT In this paper we study the long‐time stability of the Cauchy one‐leg θ$$ \theta $$‐methods for the two‐dimensional Navier‐Stokes equations. We establish the uniform dissipativity in H1$$ {H}^1 $$, in the sense that the semi‐discrete‐in‐time approximations possess a global attractor for a small enough time step, using the discrete Grönwall ...
Isabel Barrio Sanchez +2 more
wiley +1 more source
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.
Rabia Ilyas Butt +3 more
doaj +1 more source
Sharp Gronwall-Bellman type integral inequalities with delay
Electronic Journal of Qualitative Theory of Differential Equations, 2016 Various attempts have been made to give an upper bound for the solutions of the delayed version of the Gronwall-Bellman integral inequality, but the obtained estimations are not sharp.
István Győri, László Horváth
doaj +1 more source
Fractal–fractional model for analysis of tuberculosis infection using Ethiopia incidence data [PDF]
Quant BiolAbstract In this study, a fractional‐order SEIuITR $SE{I}_{u}ITR$ model was proposed to examine the transmission of tuberculosis (TB) in the community. The proposed model was rigorously examined for well‐posedness. The basic reproduction number was also derived, and the disease‐free equilibrium was obtained.
Cheneke K, Fatmawati F, Bayram M.
europepmc +2 more sources