Application of Fractional Calculus to Degenerate Hyperbolic Equations

分数阶微积分在简并双曲方程中的应用

基本信息

批准号：
03640194
负责人：
SAIGO Megumi
金额：
$ 1.02万
依托单位：
Fukuoka University
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1991
资助国家：
日本
起止时间：
1991 至 1992
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-03640194/
关键词：
Fractional calculus Degenerate hyperbolic equations Hypergeometric functions Laplace and Stieltjes transforms Axisymmetric differential operator Theory of univalent functions Mellin transform Dual integral equations 超幾何級数積分変換

项目摘要

The research on definitions and properties of generalized fractional calculus, and the investigation on solutions of the Euler-Darboux equation as an application of the fractional calculus were already published. Further, various properties of hypergeometric functions, especially behavior of the functions near the boundaries of convergence regions, were reported. In 1991 and 1992, we have the following results : On relations of products of generalized fractional integrals with the Laplace and Stieltjes transforms in the generalized function space ; On the composition of the fractional integrals and axisymmetric differential operator in potential theory ; On the problem of mapping property by the fractional integrals of the convex and starlike functions in the theory of univalent functions ; On representability of the fractional integrals by products of the Mellin and the Laplace transforms ; On applications of the fractional calculus to the H-function ; On the relation of the fractional calculus with the Laplace transform ; On solutions of dual integral equations involving the fractional calculus ; On the definition and properties of the multidimensional modified fractional calculus ; On the establishment of new integral representation formulas for multidimensional hypergeometric series ; On new integral transforms with Meijer's G-function as kernels and their convolutions ; On the application of the fractional calculus to certain probabilistic density function with multidimensional hypergeometric functions ; On the behavior near boundaries of convergence regions of the Lauricella series F_S, F_T, the Srivastava series H_C, and the Horn series H_3, G_1, G_2 ; On estimations and mapping properties of operators with power-logarithmic kernel in the generalized Holder space ; On properties in the space L_<nu,p> of integral transforms with the H-function as kernel.

关于广义分数演算的定义和特性的研究，以及对Euler-Darboux方程解决方案的解决方案的研究，作为分数演算的应用。此外，报道了高几何函数的各种特性，尤其是在收敛区域边界附近的功能的行为。在1991年和1992年，我们有以下结果：关于广义分数积分与拉普拉斯（Laplace）和stieltjes在广义函数空间中的变化的关系；潜在理论中的分数积分和轴对称差分算子的组成；关于凸的分数积分和恒星函数的映射属性的问题，在无数函数的理论中；关于梅林和拉普拉斯产物的分数积分的代表性；关于分数演算在H功能上的应用；关于分数演算与拉普拉斯变换的关系；关于涉及分数演算的双积分方程的溶液；关于多维修饰分数演算的定义和特性；建立用于多维超测量系列的新的积分表示公式；在梅耶尔（Meijer）作为内核及其卷积的新成立转变中；关于分数演算在某些概率密度函数中的应用，具有多维高几幅功能；关于Lauricella系列F_S，F_T，Srivastava系列H_C和Horn系列H_3，G_1，G_2的融合区域的近边界的行为；在广义持有器空间中具有功率 - 载体内核的操作员的估计和映射属性；在空间L_ <nu中的属性上，积分的p>用H功能作为核转换。