论文标题
Mittag-Leffler函数的自然扩展与三个无限序列相关
A natural extension of Mittag-Leffler function associated with a triple infinite series
论文作者
论文摘要
我们建立了Mittag-Leffler函数的新自然扩展，其三个变量称为“ Trivariate Mittag-Leffler函数”。可以通过使用著名的Hankel的积分来通过复杂的积分表示来表达三角形的Mittag-Leffler函数。我们还研究了该功能的单变量版本的Laplace积分关系和卷积结果。此外，我们介绍了Caputo类型中的三角形Mittag-Leffler函数的分数导数，我们还讨论了Riemann- Liouville类型的分数积分和此功能的衍生物。在物理中某些应用中，必须使用涉及不同分数订单的分数差分方程系统的三角形mittag-leffler函数与涉及不同分数订单的分数链接。因此，我们通过新定义的三角形mittag-leffler函数提供了同质和不均匀的多项分数方程的精确分析解决方案。
We establish a new natural extension of Mittag-Leffler function with three variables which is so called "trivariate Mittag-Leffler function". The trivariate Mittag-Leffler function can be expressed via complex integral representation by putting to use of the eminent Hankel's integral. We also investigate Laplace integral relation and convolution result for a univariate version of this function. Moreover, we present fractional derivative of trivariate Mittag-Leffler function in Caputo type and we also discuss Riemann- Liouville type fractional integral and derivative of this function. The link of trivariate Mittag-Leffler function with fractional differential equation systems involving different fractional orders is necessary on certain applications in physics. Thus, we provide an exact analytic solutions of homogeneous and inhomogeneous multi-term fractional differential equations by means of a newly defined trivariate Mittag-Leffler functions.
