Results 11 to 20 of about 1,849,360 (286)

Comparison of third-order fractional partial differential equation based on the fractional operators using the explicit finite difference method

Alexandria Engineering Journal, 2023
In this research paper, the third-order fractional partial differential equation (FPDE) in the sense of the Caputo fractional derivative and the Atangana-Baleanu Caputo (ABC) fractional derivative is investigated for the first time. The importance of the
Shorish Omer Abdulla, Sadeq Taha Abdulazeez, Mahmut Modanli   +2 more
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Disconjugacy for a third order linear difference equation

Computers & Mathematics with Applications, 1994
The third order linear difference equation (1) \(\Delta^ 3 y(t-1) + p(t) \Delta y(t) + q(t)y(t) = 0\) \((t \in \{a + 1, \dots, b + 1\})\) is considered. A function \(y : \{a, \dots, b + 3\} \to \mathbb{R}\) is said to have a generalized zero at \(a\) if \(y(a) = 0\) and it is said to have a generalized zero at \(t_ 0 > a\) provided either \(y(t_ 0) = 0\
Henderson, J., Peterson, A.
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Dynamics of the third order Lyness' difference equation [PDF]

Journal of Difference Equations and Applications, 2007
46 pages.
Cima, Anna, Gasull i Embid, Armengol, Mañosa, Víctor   +2 more
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Trajectory structure rule of a third-order nonlinear difference equation

上海师范大学学报. 自然科学版, 2020
In this paper the dynamics for a third-order nonlinear difference equation is considered in detail. By utilizing some beautiful mathematical skills, we describe the rule for the trajectory structure of this equation clearly and completely. The successive
PAN Zhikang, LI Xianyi
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Explicit bounds for third-order difference equations [PDF]

The ANZIAM Journal, 2006
AbstractThis paper gives explicit, applicable bounds for solutions of a wide class of third-order difference equations with nonconstant coefficients. The techniques used are readily adaptable for higher-order equations. The results extend recent work of the authors for second-order equations.
Berenhaut, Kenneth S., Goedhart, Eva G., Stević, Stevo   +2 more
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On the Global Asymptotic Stability and 4-Period Oscillation of the Third-Order Difference Equation

Journal of Applied Mathematics, 2023
The main objective of this paper is to study the global behavior and oscillation of the following third-order rational difference equation xn+1=αxnxn−1xn−2/βxn−12+γxn−22, where the initial conditions x−2,x−1,x0 are nonzero real numbers and α,β,γ are ...
M. E. Erdogan
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Oscillation of third-order half-linear neutral difference equations [PDF]

Mathematica Bohemica, 2013
The authors give oscillation criteria for the nonlinear neutral difference equations of the third order, \[ \Delta \big ( a_n\,(\Delta ^2(x_n\pm b_nx_{n-\delta }))\big )^{\alpha }+q_n\,x_{n+1-\tau }^{\alpha }=0. \] These criteria present sufficient conditions for the oscillation of every (nontrivial) solution, or the limit of the solution as \(n\to ...
Thandapani, E., Selvarangam, S.
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Oscillation for Certain Third Order Functional Delay Difference Equation

The Journal of the Indian Mathematical Society, 2021
This paper is concerned with the third order functional delay difference equation of the form Δ(CnΔ(anΔxn)) + mΣi=1pniΔxσi(n-r) + mΣi=1qnif (xσi(n-r)) = 0. We obtain some new oscillation criteria by using Riccati transformation technique. Examples are given to illustrate the results.
Jaffer, I. Mohammed Ali, Shanmugapriya, R.   +1 more
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Some representations of the general solution to a difference equation of additive type

Advances in Difference Equations, 2019
The general solution to the difference equation xn+1=axnxn−1xn−2+bxn−1xn−2+cxn−2+dxnxn−1xn−2,n∈N0, $$x_{n+1}=\frac {ax_{n}x_{n-1}x_{n-2}+bx_{n-1}x_{n-2}+cx_{n-2}+d}{x_{n}x_{n-1}x_{n-2}},\quad n\in\mathbb{N}_{0}, $$ where a,b,c∈C $a, b, c\in\mathbb{C}$, d∈
Stevo Stević
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Oscillation and Property B for Semi-Canonical Third-Order Advanced Difference Equations

Nonautonomous Dynamical Systems, 2022
In this paper, we present sufficient conditions for the third-order nonlinear advanced difference equations of the form Δ(a(n))Δ(b(n)Δy((n)))=p(n)f(y(σ(n)))\Delta \left( {a\left( n \right)} \right)\Delta \left( {b\left( n \right)\Delta y\left( {\left( n \
Chatzarakis G.E., Srinivasan R., Thandapani E.   +2 more
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