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Fractional calculus operators and their image formulas

Praveen Agarwal|최준상
대한수학회 (The Korean Mathematical Society)|2016.09|대한수학회지 (Journal of the KMS)|제53권 제5호|pp. 1183-1210

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참고문헌

키워드

Hadamard productincomplete gamma functionsgeneralized fractional calculus operatorsgeneralized incomplete hypergeometric functionsgeneralized beta functions of various kinds
주제분류수학

초록

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.

Abstract

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.

참고문헌 (62)

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