论文标题
在离散的广义Nabla分数和差异上
On discrete generalized nabla fractional sums and differences
论文作者
论文摘要
本文使用离散的Nabla卷积定理研究了一类离散的NABLA分数操作员。受此启发，我们定义了Riemann-Liouville和Caputo类型的离散的Nabla分数和差异。在此过程中，我们在Ferreira \ cite {ferreira}引入的广义离散的三角分数和拟议的离散通用的Nabla分数操作员之间通过双重身份提供了关系。另外，我们提出了一些测试示例，以证明这种关系是合理的。此外，我们证明了定义的离散通用Nabla分数运算符的微积分的基本定理。受上述操作员的启发，我们定义了本文末尾的离散的Nabla Atangana-Baleanu样（或类似caputo-fabrizio）的分数和差异。
This article investigates a class of discrete nabla fractional operators by using the discrete nabla convolution theorem. Inspired by this, we define the discrete generalized nabla fractional sum and differences of Riemann-Liouville and Caputo types. In the process, we give a relationship between the generalized discrete delta fractional operators introduced by Ferreira \cite{Ferreira} and the proposed discrete generalized nabla fractional operators via the dual identities. Also, we present some test examples to justify the relationship. Moreover, we prove the fundamental theorem of calculus for the defined discrete generalized nabla fractional operators. Inspired by the above operators, we define discrete generalized nabla Atangana-Baleanu-like (or Caputo-Fabrizio-like) fractional sum and differences at the end of the article.
