Hadi Sarem H, Challab Khalid A, Ali Ali Hasan, Alatawi Abdullah A
Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah 61001, Iraq.
Department of Business Management, Al-imam University College, Balad 34011, Iraq.
MethodsX. 2024 Nov 17;13:103061. doi: 10.1016/j.mex.2024.103061. eCollection 2024 Dec.
This paper proposes a new extension of the well-known -special function, which is called -function. We introduce this function by drawing inspiration from exponential function. This new special function is studied from a variety of analytical perspectives, including differential and integral operators. Furthermore, the -Weyl fractional integral operator involving the -function is studied. These classes are defined by utilizing a new q-differential operator.•The - function is provided.•The derivative and integral formulas of the -function are studied.•An application of the -Weyl fractional integral operator associated with the -function is investigated.
本文提出了一种著名的 - 特殊函数的新扩展，称为 - 函数。我们通过从指数函数中汲取灵感来引入此函数。从包括微分和积分算子在内的各种分析角度对这种新的特殊函数进行了研究。此外，还研究了涉及 - 函数的 - 魏尔分数积分算子。这些类别是利用一个新的q - 微分算子定义的。
给出了 - 函数。
研究了 - 函数的导数和积分公式。
研究了与 - 函数相关的 - 魏尔分数积分算子的一个应用。
