Nowadays most researchers have been focused on fractional calculus because it has been proved that fractional derivatives could describe most phenomena better than usual derivations. Numerical parts of fractional calculus such as q-derivations are considered by researchers. In this work, our aim is to review the existence of solution for an m-dimensional system of fractional q-differential inclusions via sum of two multi-term functions under some boundary conditions on the time scale $\mathbb{T}_{t_{0}}= \{ t : t =t_{0}q^{n}\}\cup\{0\}$ , where $n\geq1$ , $t_{0} \in\mathbb{R}$ , and $q \in(0,1)$ . By using the Banach contraction principle and some sufficient conditions, we guarantee the existence of solutions for the system of q-differential inclusions. Also, we provide an example, some algorithms, and a figure to illustrate our main result.

中文翻译：

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在时间尺度上通过两个多项函数之和组成的分数阶q-微分包含系统

如今，大多数研究者将注意力集中在分数演算上，因为已证明分数导数可以比通常的推导更好地描述大多数现象。研究人员考虑了分数微积分的数值部分，例如q导数。在这项工作中，我们的目的是通过在时间尺度$ \ mathbb {T} _ {t_上，在某些边界条件下，通过两个多项函数的和，回顾分数维-微分包含的m维系统的解的存在性{0}} = \ {t：t = t_ {0} q ^ {n} \} \ cup \ {0 \} $，其中$ n \ geq1 $，$ t_ {0} \ in \ mathbb {R} $和$ q \ in（0,1）$。通过使用Banach压缩原理和一些充分的条件，我们保证了q微分包含系统的解的存在。另外，我们提供一个示例，一些算法和一个图来说明我们的主要结果。