关于delta和nabla Caputo分数差分和对偶恒等式
On delta and nabla Caputo fractional differences and dual identities
摘要：
我们研究两种类型的双重身份的Caputo分数的差异。第一种类型涉及nabla和delta类型的分数和与差。第二种类型由Q-算子表示，涉及左和右分数和和差。引入了两种类型的卡普托分数差，定义了其中一种（对偶差），使其服从所研究的对偶恒等式。通过求解Caputo型线性分数阶差分方程，研究了Rieamnn和Caputo分数阶差分之间的关系，确定了Delta和nabla离散Mittag-Leffler函数.对Caputo分数阶差分也得到了nabla分部分部积分法公式。
英文摘要：
We Investigate two types of dual identities for Caputo fractional differences. The first type relates nabla and delta type fractional sums and differences. The second type represented by the Q-operator relates left and right fractional sums and differences. Two types of Caputo fractional differences are introduced, one of them (dual one) is defined so that it obeys the investigated dual identities. The relation between Rieamnn and Caputo fractional differences is investigated and the delta and nabla discrete Mittag-Leffler functions are confirmed by solving Caputo type linear fractional difference equations. A nabla integration by parts formula is obtained for Caputo fractional differences as well.
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