Results 51 to 60 of about 610,482 (163)
On the Hyers-Ulam Stability of Differential Equations of Second Order
Abstract and Applied Analysis, 2014 By using of the Gronwall inequality, we prove the Hyers-Ulam stability of differential equations of second order with initial conditions.
Qusuay H. Alqifiary, Soon-Mo Jung
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A new approach to interval-valued inequalities
Advances in Difference Equations, 2020 The objective of this work is to advance and simplify the notion of Gronwall’s inequality. By using an efficient partial order and concept of gH-differentiability on interval-valued functions, we investigate some new variants of Gronwall type ...
Awais Younus +4 more
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Concept and application of interval-valued fractional conformable calculus
Alexandria Engineering Journal, 2022 This paper introduces a new concept of Caputo type interval-valued fractional conformable calculus. Based on this, some theorems and properties related to fractional conformable calculus are presented.
Lihong Zhang +3 more
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On a Stieltjes version of Gronwall’s inequality [PDF]
Proceedings of the American Mathematical Society, 1981 A unified formulation of Gronwall’s inequality ( GI ) ({\text {GI}}) for certain Stieltjes integrals is presented. An advantage in using Stieltjes integrals lies in the fact that some of the "continuous" and "discrete" versions of the inequality may be obtained as a consequence of the same ...
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International Journal for Numerical Methods in Fluids, EarlyView.This study investigates the impact of uncertain parameters on Navier–Stokes equations coupled with heat transfer using the Intrusive Polynomial Chaos Method (IPCM). Sensitivity equations are formulated for key input parameters, such as viscosity and thermal diffusivity, and solved numerically using the Finite Element‐Volume method.
N. Nouaime +3 more
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Analysis of L1-difference methods for time-fractional nonlinear parabolic problems with delay [PDF]
, 2017 This work is concerned with numerical solutions of time-fractional nonlinear parabolic problems by a class of L1-difference methods. The analysis of L1 methods for timefractional nonlinear problems with delay is limited mainly due to the lack of a ...
De Staelen, Rob, Hendy, Ahmed S.
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On Gronwall and Wendroff type inequalities [PDF]
Proceedings of the American Mathematical Society, 1983 It is shown how Gronwall’s Lemma and the extension to many variables given by W. Walter may be derived using the simple method of recursion. This same method is used to extend this result and to derive a more general Wendroff type inequality. Upper and lower bounds for the Neumann series in the case of two independent variables are given.
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Mathematical Methods in the Applied Sciences, EarlyView.A highly accurate numerical method is given for the solution of boundary value problem of generalized Bagley‐Torvik (BgT) equation with Caputo derivative of order 0<β<2$$ 0<\beta <2 $$ by using the collocation‐shooting method (C‐SM). The collocation solution is constructed in the space Sm+1(1)$$ {S}_{m+1}^{(1)} $$ as piecewise polynomials of degree at ...
Suzan Cival Buranay +2 more
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Well-posedness of time-fractional, advection-diffusion-reaction equations
, 2019 We establish the well-posedness of an initial-boundary value problem for a general class of time-fractional, advection-diffusion-reaction equations, allowing space- and time-dependent coefficients as well as initial data that may have low regularity. Our
Ali, Raed +3 more
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Gronwall inequalities via Picard operators
Annals of the Alexandru Ioan Cuza University - Mathematics, 2012 Let \(A\) be an operator on an ordered set \(X\) such that the equation \(A(x)=x\) has a unique solution \(x^\ast\). The second author raised the following problem in his study of Picard operators [Sci. Math. Jpn. 58, No. 1, 191--219 (2003; Zbl 1031.47035)]: Find the conditions under which \(x\leq A(x)\), respectively \(x\geq A(x)\), implies that \(x ...
Lungu, Nicolaie, Rus, Ioan A.
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