论文标题
Green的功能和具有DIRICHLET边界条件的非线性分数隐式差方程的解决方案的存在
Green's Functions and Existence of Solutions of Nonlinear Fractional Implicit Difference Equations with Dirichlet Boundary Conditions
论文作者
论文摘要
本文致力于推断绿色函数的表达与一般恒定系数的分数方程相关的一般恒定系数与Dirichlet条件耦合。在这种情况下，由于某些分数运算符的点，我们存在隐式分数方程。这样的属性使计算和管理绿色功能的表达变得更加复杂。与从有限总和遵循的明确情况相反，这种表达是从一系列无穷术语中得出的。这种表达将从整数的时间尺度上的拉普拉斯变换推导。最后，我们通过合适的固定点定理证明了非线性问题的两个存在结果。
This article is devoted to deduce the expression of the Green's function related to a general constant coefficients fractional difference equation coupled to Dirichlet conditions. In this case, due to the points where some of the fractional operators is applied, we are in presence of a implicit fractional difference equation. Such property makes it more complicated to calculate and manage the expression of the Green's function. Such expression, on the contrary to the explicit case where it follows from finite sums, is deduced from series of infinity terms. Such expression will be deduced from the Laplace transform on the time scales of the integers. Finally, we prove two existence results for nonlinear problems, via suitable fixed point theorems.
