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Fractional calculus operators and their image formulas

机译:分数微积分算子及其图像公式

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During the past four decades or so, due mainly to a wide range of applications from natural sciences to social sciences, the so-called fractional calculus has attracted an enormous attention of a large number of researchers. Many fractional calculus operators, especially, involving various special functions, have been extensively investigated and widely applied. Here, in this paper, in a systematic manner, we aim to establish certain image formulas of various fractional integral operators involving diverse types of generalized hypergeometric functions, which are mainly expressed in terms of Hadamard product. Some interesting special cases of our main results are also considered and relevant connections of some results presented here with those earlier ones are also pointed out.
机译:在过去的四十年左右的时间里,主要由于从自然科学到社会科学的广泛应用,所谓的分数演算吸引了众多研究人员的极大关注。尤其是涉及许多特殊功能的许多分数微积分算子已经得到了广泛的研究和广泛的应用。在这里,本文以系统的方式,旨在建立涉及各种类型的广义超几何函数的各种分数积分算子的某些图像公式,这些图像公式主要以Hadamard乘积表示。还考虑了一些主要结果有趣的特殊情况,并指出了此处介绍的一些结果与早期结果的相关联系。

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