Fractional calculus for power functions and eigenvalues of the fractional Laplacian

被引：0
|
作者：
Bartłlomiej Dyda
机构：
[1] University of Bielefeld,Faculty of Mathematics
[2] Wrocław University of Technology,Institute of Mathematics and Computer Science
来源：
Fractional Calculus and Applied Analysis | 2012年 / 15卷
关键词：
fractional Laplacian; ball; killed stable process; eigenvalue; power function; hypergeometric function; Primary 35P15; Secondary 60G52, 31C25;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We calculate the fractional Laplacian Δα/2 for functions of the form u(x) = (1 − |x|2)+p and v(x) = xdu(x). As an application, we estimate the first eigenvalues of the fractional Laplacian in a ball.
引用
收藏
页码：536 / 555
页数：19
相关论文
共 50 条
  • [21] On the Decomposition of Solutions: From Fractional Diffusion to Fractional Laplacian
    Yulong Li
    Fractional Calculus and Applied Analysis, 2021, 24 : 1571 - 1600
  • [22] Fractional p-eigenvalues
    Franzina, Giovanni
    Palatucci, Giamplero
    RIVISTA DI MATEMATICA DELLA UNIVERSITA DI PARMA, 2014, 5 (02): : 373 - 386
  • [23] Implementation of Special Mathematical Functions for Fractional Calculus using DSP Processor
    Singhaniya, Navin G.
    Patil, Mukesh D.
    Vyawahare, Vishwesh A.
    2015 IEEE INTERNATIONAL CONFERENCE ON INFORMATION PROCESSING (ICIP), 2015, : 811 - 816
  • [24] Some bifurcation results for fractional Laplacian problems
    Chhetri, Maya
    Girg, Petr
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2020, 191
  • [25] Fractional Laplacian with singular drift
    Jakubowski, Tomasz
    STUDIA MATHEMATICA, 2011, 207 (03) : 257 - 273
  • [26] BOUNDED RESONANT PROBLEMS DRIVEN BY FRACTIONAL LAPLACIAN
    Chen, Yutong
    Su, Jiabao
    TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 2021, 57 (02) : 635 - 661
  • [27] Mellin definition of the fractional Laplacian
    Gianni Pagnini
    Claudio Runfola
    Fractional Calculus and Applied Analysis, 2023, 26 : 2101 - 2117
  • [28] A variable diffusivity fractional Laplacian
    Ervin, V. J.
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2025, 547 (01)
  • [29] Fractional Laplacian with Hardy potential
    Bogdan, Krzysztof
    Grzywny, Tomasz
    Jakubowski, Tomasz
    Pilarczyk, Dominika
    COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2019, 44 (01) : 20 - 50
  • [30] Variational Inequalities for the Fractional Laplacian
    Roberta Musina
    Alexander I. Nazarov
    Konijeti Sreenadh
    Potential Analysis, 2017, 46 : 485 - 498
12345