Baleanu D, Agarwal P, Purohit S D
Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah 21589, Saudi Arabia ; Department of Mathematics and Computer Sciences, Faculty of Art and Sciences, Cankaya University, Ankara, Turkey ; Institute of Space Sciences, P.O. Box MG-23, 76900 Magurele Bucharest, Romania.
Department of Mathematics, Anand International College of Engineering, Jaipur 303012, India.
ScientificWorldJournal. 2013 Nov 28;2013:567132. doi: 10.1155/2013/567132. eCollection 2013.
We apply generalized operators of fractional integration involving Appell's function F 3(·) due to Marichev-Saigo-Maeda, to the product of the generalized Bessel function of the first kind due to Baricz. The results are expressed in terms of the multivariable generalized Lauricella functions. Corresponding assertions in terms of Saigo, Erdélyi-Kober, Riemann-Liouville, and Weyl type of fractional integrals are also presented. Some interesting special cases of our two main results are presented. We also point out that the results presented here, being of general character, are easily reducible to yield many diverse new and known integral formulas involving simpler functions.
我们将由马里切夫 - 斋藤 - 前田给出的涉及Appell函数F₃(·)的分数阶积分广义算子，应用于由巴里茨给出的第一类广义贝塞尔函数的乘积。结果用多变量广义劳里切拉函数表示。还给出了关于斋藤、埃尔德利 - 科贝尔、黎曼 - 刘维尔和外尔型分数阶积分的相应结论。给出了我们两个主要结果的一些有趣的特殊情况。我们还指出，这里给出的结果具有一般性，很容易化简得到许多涉及更简单函数的各种新的和已知的积分公式。
