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Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.Water contamination is a crucial area of study that has drawn significant attention from researchers and environmentalists due to its profound impact on humans, animals, and plants. It is equally harmful as air and soil contamination and is closely linked to both.
Pasquini Fotsing Soh +4 more
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The generalized Hyers–Ulam–Rassias stability of a cubic functional equation
Journal of Mathematical Analysis and Applications, 2002 The authors consider the functional equation \[ f(2x+y) +f(2x-y)=2f(x+y)+ 2f(x-y)+12f(x). \] They determine the general solution, which is of the form \(f(x)= B(x,x,x)\) where \(B\) is symmetric and additive in each variable. Moreover they investigate the stability properties of this equation.
Jun, Kil-Woung, Kim, Hark-Mahn
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Controllability and Hyers-Ulam stability results of initial value problems for fractional differential equations via generalized proportional-Caputo fractional derivative [PDF]
, 2021 Mohamed I. Abbas
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A Generalization of the Hyers–Ulam–Rassias Stability of Jensen's Equation
Journal of Mathematical Analysis and Applications, 1999 The following generalization of the stability of the Jensen's equation in the spirit of Hyers-Ulam-Rassias is proved: Let \(V\) be a normed space, \(X\) -- a Banach space, \(pa\). For the case \(p>1\) a corresponding result is obtained.
Lee, Yang-Hi, Jun, Kil-Woung
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Hyers-Ulam Stability and Existence of Solutions for Nigmatullin’s Fractional Diffusion Equation
Advances in Mathematical Physics, 2017 We discuss stability of time-fractional order heat conduction equations and prove the Hyers-Ulam and generalized Hyers-Ulam-Rassias stability of time-fractional order heat conduction equations via fractional Green function involving Wright function.
Zhuoyan Gao, JinRong Wang
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Mathematics, 2019 In this paper, the Hyers–Ulam stability of linear Caputo–Fabrizio fractional differential equation is established using the Laplace transform method.
Kui Liu +3 more
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International Journal of Analysis and Applications, 2019 In this paper, we prove the generalized Hyers-Ulam-Rassias stability of the bi-Cauchy-Jensen functional equation and the bi-additive-quadratic functional equation in paranormed spaces.
Prondanai Kaskasem, Chakkrid Klin-eam
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The Stability of a Quadratic Functional Equation with the Fixed Point Alternative
Abstract and Applied Analysis, 2009 Lee, An and Park introduced the quadratic functional equation f(2x+y)+f(2x−y)=8f(x)+2f(y) and proved the stability of the quadratic functional equation in the spirit of Hyers, Ulam and Th. M. Rassias.
Choonkil Park, Ji-Hye Kim
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