Solutions structures for some systems of fractional difference equations

M. Almatrafi
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引用次数: 13

Abstract

It is a well-known fact that the majority of rational difference equations cannot be solved theoretically. As a result, some scientific experts use manual iterations to obtain the exact solutions of some of these equations. In this paper, we obtain the fractional solutions of the following systems of difference equations: xn+1 = xn−1yn−3 yn−1 (−1− xn−1yn−3) , yn+1 = yn−1xn−3 xn−1 (±1± yn−1xn−3) , n = 0, 1, ..., where the initial data x−3, x−2, x−1, x0, y−3, y−2, y−1 and y0 are arbitrary non-zero real numbers. All solutions will be depicted under specific initial conditions.
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一类分数阶差分方程组的解结构
众所周知,大多数有理差分方程都无法从理论上求解。因此,一些科学专家使用手动迭代来获得其中一些方程的精确解。在本文中,我们得到了以下差分方程组的分式解:xn+1=xn−1yn−3 yn−1(−1−xn−1 yn−3),yn+1=yn−1xn−3 xn−3(±1±yn−1xn-3),n=0,1。。。,其中初始数据x−3、x−2、x−1、x0、y−3、y−2、y−1和y0是任意非零实数。所有解决方案将在特定的初始条件下进行描述。
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发文量
10
审稿时长
8 weeks
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