广义扩展Mittag-Leffler函数及其关于积分变换和分数阶微积分的性质

IF 1.1 Q2 EDUCATION & EDUCATIONAL RESEARCH

Research in Mathematics Education Pub Date : 2023-06-21 DOI:10.1080/27684830.2023.2220205

A. Padma, M. Ganeshwara Rao, Biniyam Shimelis

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引用次数: 1

摘要

本文旨在通过扩展Beta函数引入扩展广义Mittag-Leffler函数(EGMLF)，并得到其一定的积分和微分表示形式。进一步，我们给出了Riemann—Liouville分数阶积分和微分算子的一些公式。此外，我们还推导了各种积分变换，包括欧拉变换、拉普拉斯变换、惠特卡变换和k变换。算子和变换图像用Wright广义超几何-超几何型函数表示。还考虑了主要结果的有趣的特殊情况。

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Generalized extended Mittag-Leffler function and its properties pertaining to integral transforms and fractional calculus

We aim to introduce extended generalized Mittag-Leffler function (EGMLF) via the extended Beta function and obtain certain integral and differential representation of them. Further, we present some formulas of the Riemann-–Liouville fractional integration and differentiation operators. Also, we derive various integral transforms, including Euler transform, Laplace transform, Whittakar transform and K-transform. The operator and transform images are expressed in terms of the Wright generalized hypergoemetrichypergeometric type function. Interesting special cases of the main results are also considered.

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来源期刊

Research in Mathematics Education EDUCATION & EDUCATIONAL RESEARCH-

CiteScore

3.00

自引率

15.40%

发文量