一类Riemann-Loiuville型分数阶差分方程解对初值的连续依赖性

Continuous Dependence of Solutions on Initial Data for a Class of Riemann-Loiuville Fractional Difference Equations

针对一类Riemann-Loiuville型分数阶差分方程,利用分数阶差分性质,构造了一个Volterra和分方程,再利用离散分数阶Gronwall不等式和离散Mittag-Leffler函数的性质,在合适的条件下获得了这个方程解对初值的连续依赖性,并用新方法证明了解的唯一性。

This paper is concerned with a class of Riemann-Loiuville fractional difference equations. Volterra Summation Decomposition Equation is obtained by using of properties of fractional differences. Under the suitable conditions, the continuous dependence of solutions on initial data is derived by resorting to the discrete fractional Gronwall inequality and properties of the discrete Mittag-Leffler function. A new method is given to prove the uniqueness of solutions.