论文标题
与双方面的Hilfer分数$ Q $衍生有关的分数cauchy问题
Fractional Cauchy problems associated with the bi-ordinal Hilfer fractional $q$-derivative
论文作者
论文摘要
为了研究针对分数q差异方程的cauchy型问题的解决方案的存在和独特性，这是双方向分数q衍生的，这是Hilfer分数Q衍生物的扩展。一种方法是基于非线性考奇型问题与第二种非线性伏特拉q综合方程的等效性。应用Banach固定点定理的类似物，我们证明了溶液的独特性和存在。此外，我们为线性案例的库奇问题的Q-Analog提供了明确的解决方案。
To study the existence and uniqueness of solutions to Cauchy-type problems for fractional q-difference equations with the bi-ordinal Hilfer fractional q-derivative which is an extension of the Hilfer fractional q-derivative. An approach is based on the equivalence of the nonlinear Cauchy-type problem with a nonlinear Volterra q-integral equation of the second kind. Applying an analog of Banach fixed point theorem we prove the uniqueness and the existence of the solution. Moreover, we present an explicit solution to the q-analog of the Cauchy problem for the linear case.
