Results 1 to 10 of about 530 (65)
A certain class of fractional difference equations with damping: Oscillatory properties
Demonstratio Mathematica, 2023 In this study, we have investigated the oscillatory properties of the following fractional difference equation: ∇α+1χ(κ)⋅∇αχ(κ)−p(κ)г(∇αχ(κ))+q(κ)G∑μ=κ−α+1∞(μ−κ−1)(−α)χ(μ)=0,{\nabla }^{\alpha +1}\chi \left(\kappa )\cdot {\nabla }^{\alpha }\chi \left ...
Arundhathi Sivakumar +3 more
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Open Mathematics, 2022 In this article, we consider a discrete nonlinear third-order boundary value problem Δ3u(k−1)=λa(k)f(k,u(k)),k∈[1,N−2]Z,Δ2u(η)=αΔu(N−1),Δu(0)=−βu(0),u(N)=0,\left\{\phantom{\rule[-1.25em]{}{0ex}}\begin{array}{l}{\Delta }^{3}u\left(k-1)=\lambda a\left(k)f ...
Li Huijuan +2 more
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Asymptotic behavior of solutions of a second-order nonlinear discrete equation of Emden-Fowler type
Advances in Nonlinear Analysis, 2023 The article investigates a second-order nonlinear difference equation of Emden-Fowler type Δ2u(k)±kαum(k)=0,{\Delta }^{2}u\left(k)\pm {k}^{\alpha }{u}^{m}\left(k)=0, where kk is the independent variable with values k=k0,k0+1,…k={k}_{0},{k}_{0}+1,\ldots ...
Diblík Josef, Korobko Evgeniya
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Open Mathematics, 2021 In this paper, we discuss the existence of positive solutions to a discrete third-order three-point boundary value problem. Here, the weight function a(t)a\left(t) and the Green function G(t,s)G\left(t,s) both change their sign.
Cao Xueqin, Gao Chenghua, Duan Duihua
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A unified approach for novel estimates of inequalities via discrete fractional calculus techniques
Alexandria Engineering Journal, 2022 In this article, we introduce the discrete fractional sum equations and inequalities. Some new generalized Grüss type discrete fractional sum inequalities are developed. We employ a nabla or backward difference; we employ the Riemann-Liouville definition
Samaira Naz, Yu-Ming Chu
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Open Mathematics, 2022 In this article, we are concerned with the periodic solutions of first-order difference equation Δu(t−1)=f(t,u(t))−s,t∈Z,(P)\Delta u\left(t-1)=f\left(t,u\left(t))-s,\hspace{1em}t\in {\mathbb{Z}},\hspace{1.0em}\hspace{1.0em}\left(P) where s∈Rs\in {\mathbb{
Zhao Jiao, Ma Ruyun
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Pharmacokinetics and Pharmacodynamics Models of Tumor Growth and Anticancer Effects in Discrete Time
Computational and Mathematical Biophysics, 2020 We study the h-discrete and h-discrete fractional representation of a pharmacokinetics-pharmacodynamics (PK-PD) model describing tumor growth and anticancer effects in continuous time considering a time scale h0, where h > 0.
Atıcı Ferhan M. +4 more
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Multidimensional sampling theorems for multivariate discrete transforms
Advances in Difference Equations, 2021 This paper is devoted to the establishment of two-dimensional sampling theorems for discrete transforms, whose kernels arise from second order partial difference equations.
H. A. Hassan
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Do All Integrable Evolution Equations Have the Painlev\'e Property? [PDF]
, 2007 We examine whether the Painleve property is necessary for the integrability of partial differential equations (PDEs). We show that in analogy to what happens in the case of ordinary differential equations (ODEs) there exists a class of PDEs, integrable ...
Grammaticos, Basil +2 more
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Nabla Discrete fractional Calculus and Nabla Inequalities [PDF]
, 2009 Here we define a Caputo like discrete nabla fractional difference and we produce discrete nabla fractional Taylor formulae for the first time. We estimate their remaiders.
Anastassiou, George A.
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