论文标题
分数Q-差分微积分中某些cauchy型问题的存在和独特性
Existence and uniqueness of some Cauchy Type Problems in fractional q-difference calculus
论文作者
论文摘要
在本文中，我们得出了足够的条件 解决Cauchy型Q分数问题的解决方案（涉及Riemann-Liouville类型的分数Q衍生物） 对于某些非线性微分方程。关键技术首先证明了这种cauchy型Q分数问题等效于相应的volterra Q综合方程。此外，我们定义了Hilfer分数或复合分数衍生物操作员的$ Q $ - 动态，并证明了上述类似的新等价，存在和唯一性结果。最后，提出了一些示例，以说明我们的主要结果，在我们甚至可以为这些独特解决方案提供具体配方的情况下。
In this paper we derive a sufficient condition for the existence of a unique solution of a Cauchy type q-fractional problem (involving the fractional q-derivative of Riemann-Liouville type) for some nonlinear differential equations. The key technique is to first prove that this Cauchy type q-fractional problem is equivalent to a corresponding Volterra q-integral equation. Moreover, we define the $q$-analogue of the Hilfer fractional derivative or composite fractional derivative operator and prove some similar new equivalence, existence and uniqueness results as above. Finally, some examples are presented to illustrate our main results in cases where we can even give concrete formulas for these unique solutions.
