$\require{mediawiki-texvc}$

연합인증

연합인증 가입 기관의 연구자들은 소속기관의 인증정보(ID와 암호)를 이용해 다른 대학, 연구기관, 서비스 공급자의 다양한 온라인 자원과 연구 데이터를 이용할 수 있습니다.

이는 여행자가 자국에서 발행 받은 여권으로 세계 각국을 자유롭게 여행할 수 있는 것과 같습니다.

연합인증으로 이용이 가능한 서비스는 NTIS, DataON, Edison, Kafe, Webinar 등이 있습니다.

한번의 인증절차만으로 연합인증 가입 서비스에 추가 로그인 없이 이용이 가능합니다.

다만, 연합인증을 위해서는 최초 1회만 인증 절차가 필요합니다. (회원이 아닐 경우 회원 가입이 필요합니다.)

연합인증 절차는 다음과 같습니다.

최초이용시에는
ScienceON에 로그인 → 연합인증 서비스 접속 → 로그인 (본인 확인 또는 회원가입) → 서비스 이용

그 이후에는
ScienceON 로그인 → 연합인증 서비스 접속 → 서비스 이용

연합인증을 활용하시면 KISTI가 제공하는 다양한 서비스를 편리하게 이용하실 수 있습니다.

On fractional heat equation 원문보기

Fractional calculus & applied analysis, v.24 no.1, 2021년, pp.73 - 87  

Kochubei, Anatoly N. ,  Kondratiev, Yuri ,  da Silva, José ,  Luís

Abstract ▼ AI-Helper 아이콘AI-Helper

AbstractIn this paper, the long-time behavior of the Cesaro mean of the fundamental solution for fractional Heat equation corresponding to random time changes in the Brownian motion is studied. We consider both stable subordinators leading to equations with the Caputo-Djrbashian fractional derivativ...

주제어

#Primary 35R11   #Secondary 26A33   #60G22   #general fractional derivative   #subordination   #heat equation   #long time behavior  

참고문헌 (20)

  1. [1] J. Arias-de Reyna, On the theorem of Frullani. Proc. Amer. Math. Soc . 109 , No 1 (1990), 165-175; DOI: 10.1090/S0002-9939-1990-1007485-4 . Arias-de Reyna J. On the theorem of Frullani Proc. Amer. Math. Soc 109 No 1 1990 165 175 10.1090/S0002-9939-1990-1007485-4 

  2. [2] M. Abramowitz and I. A. Stegun (Eds.), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables . Dover Publications Inc., New York, 1992; Reprint of the 1972 Edition. Abramowitz M. Stegun I. A. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables Dover Publications Inc New York 1992 Reprint of the 1972 Edition 

  3. [3] J. Bertoin, Levy Processes , Vol. 121 of Cambridge Tracts in Mathematics. Cambridge University Press, Cambridge, 1996. Bertoin J. Levy Processes Vol. 121 of Cambridge Tracts in Mathematics Cambridge University Press Cambridge 1996 

  4. [4] N. H. Bingham, C. M. Goldie, and J. L. Teugels, Regular Variation , Vol. 27 of Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge, 1987. Bingham N. H. Goldie C. M. Teugels J. L. Regular Variation Vol. 27 of Encyclopedia of Mathematics and its Applications Cambridge University Press Cambridge 1987 

  5. [5] N. H. Bingham, Limit theorems for occupation times of Markov processes. Z. Wahrsch. Verw. Gebiete 17 (1971), 1-22; DOI: 10.1007/BF00538470 . Bingham N. H. Limit theorems for occupation times of Markov processes Z. Wahrsch. Verw. Gebiete 17 1971 1 22 10.1007/BF00538470 

  6. [6] B. Baeumer and M. M. Meerschaert, Stochastic solutions for fractional Cauchy problems. Fract. Calc. Appl. Anal . 4 , No 4 (2001), 481-500. Baeumer B. Meerschaert M. M. Stochastic solutions for fractional Cauchy problems Fract. Calc. Appl. Anal 4 No 4 2001 481 500 

  7. [7] Z.-Q. Chen, Time fractional equations and probabilistic representation. Chaos Solitons Fractals 102 (2017), 168-174; DOI: 10.1016/j.chaos.2017.04.029 . Chen Z.-Q. Time fractional equations and probabilistic representation Chaos Solitons Fractals 102 2017 168 174 10.1016/j.chaos.2017.04.029 

    상세보기

  8. [8] Z.-Q. Chen, P. Kim, T. Kumagai, and J. Wang, Heat kernel estimates for time fractional equations. Forum Math . 30 , No 5 (2018), 1163-1192; DOI: 10.1515/forum-2017-0192 . Chen Z.-Q. Kim P. Kumagai T. Wang J. Heat kernel estimates for time fractional equations Forum Math 30 No 5 2018 1163 1192 10.1515/forum-2017-0192 

  9. [9] A. Erdelyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi (Eds.), Tables of Integral Transforms, Vol. I . McGraw-Hill Book Company, Inc., New York-Toronto-London, 1954. Erdelyi A. Magnus W. Oberhettinger F. Tricomi F. G. Tables of Integral Transforms, Vol. I McGraw-Hill Book Company, Inc New York-Toronto-London 1954 

  10. [10] A. N. Kochubei, Yu. G. Kondratiev, and J. L. da Silva, Random time change and related evolution equations. Time asymptotic behavior. Stochastics and Dynamics 4 (2019), Art. 2050034, 24 pp.; DOI: 10.1142/S0219493720500343 . Kochubei A. N. Kondratiev Yu. G. da Silva J. L. Random time change and related evolution equations. Time asymptotic behavior Stochastics and Dynamics 4 2019 Art. 2050034 24 10.1142/S0219493720500343 

  11. [11] A. N. Kochubei, General fractional calculus, evolution equations, and renewal processes. Integral Equations Operator Theory 71 , No 4 (2011), 583-600; DOI: 10.1007/s00020-011-1918-8 . Kochubei A. N. General fractional calculus, evolution equations, and renewal processes Integral Equations Operator Theory 71 No 4 2011 583 600 10.1007/s00020-011-1918-8 

  12. [12] Y.-C. Li, R. Sato, and S.-Y. Shaw, Ratio Tauberian theorems for positive functions and sequences in Banach lattices. Positivity 11 , No 3 (2007), 433-447; DOI: 10.1007/s11117-007-2085-7 . Li Y.-C. Sato R. Shaw S.-Y. Ratio Tauberian theorems for positive functions and sequences in Banach lattices Positivity 11 No 3 2007 433 447 10.1007/s11117-007-2085-7 

  13. [13] A. Mimica, Heat kernel estimates for subordinate Brownian motions. Proc. Lond. Math. Soc. (3) 113 , No 5 (2016), 627-648; DOI: 10.1112/plms/pdw043 . Mimica A. Heat kernel estimates for subordinate Brownian motions Proc. Lond. Math. Soc. (3) 113 No 5 2016 627 648 10.1112/plms/pdw043 

  14. [14] F. Mainardi, A. Mura, and G. Pagnini, The M -Wright function in time-fractional diffusion processes: A tutorial survey. Int. J. Differential Equ . 2010 (2010), Art. 104505, 29 pp.; DOI: 10.1155/2010/104505 . Mainardi F. Mura A. Pagnini G. The M -Wright function in time-fractional diffusion processes: A tutorial survey Int. J. Differential Equ 2010 2010 Art. 104505 29 10.1155/2010/104505 

  15. [15] M. M. Meerschaert and H.-P. Scheffler, Limit theorems for continuous-time random walks with infinite mean waiting times. J. Appl. Probab . 41 , No 3 (2004), 623-638; DOI: 10.1239/jap/1091543414 . Meerschaert M. M. Scheffler H.-P. Limit theorems for continuous-time random walks with infinite mean waiting times J. Appl. Probab 41 No 3 2004 623 638 10.1239/jap/1091543414 

  16. [16] M. M. Meerschaert and H.-P. Scheffler, Triangular array limits for continuous time random walks. Stochastic Process. Appl . 118 , No 9 (2008), 1606-1633; DOI: 10.1016/j.spa.2007.10.005 . Meerschaert M. M. Scheffler H.-P. Triangular array limits for continuous time random walks Stochastic Process. Appl 118 No 9 2008 1606 1633 10.1016/j.spa.2007.10.005 

  17. [17] M. Magdziarz and R. L. Schilling, Asymptotic properties of Brownian motion delayed by inverse subordinators. Proc. Amer. Math. Soc . 143 , No 10 (2015), 4485-4501; DOI: 10.1090/proc/12588 . Magdziarz M. Schilling R. L. Asymptotic properties of Brownian motion delayed by inverse subordinators Proc. Amer. Math. Soc 143 No 10 2015 4485 4501 10.1090/proc/12588 

  18. [18] E. Seneta, Regularly Varying Functions , Vol. 508 of Lect. Notes Math., Springer, 1976. Seneta E. Regularly Varying Functions Vol. 508 of Lect. Notes Math Springer 1976 

  19. [19] R. L. Schilling, R. Song, and Z. Vondraek, Bernstein Functions: Theory and Applications . De Gruyter Studies in Math., De Gruyter, Berlin, 2 Edition, 2012. Schilling R. L. Song R. Vondraek Z. Bernstein Functions: Theory and Applications De Gruyter Studies in Math., De Gruyter Berlin 2 2012 

  20. [20] B. Toaldo, Convolution-type derivatives, hitting-times of subordinators and time-changed C 0 -semigroups. Potential Anal . 42 , No 1 (2015), 115-140; DOI: 10.1007/s11118-014-9426-5 . Toaldo B. Convolution-type derivatives, hitting-times of subordinators and time-changed C 0 -semigroups Potential Anal 42 No 1 2015 115 140 10.1007/s11118-014-9426-5 

관련 콘텐츠

오픈액세스(OA) 유형

BRONZE

출판사/학술단체 등이 한시적으로 특별한 프로모션 또는 일정기간 경과 후 접근을 허용하여, 출판사/학술단체 등의 사이트에서 이용 가능한 논문

저작권 관리 안내
섹션별 컨텐츠 바로가기

AI-Helper ※ AI-Helper는 오픈소스 모델을 사용합니다.

AI-Helper 아이콘
AI-Helper
안녕하세요, AI-Helper입니다. 좌측 "선택된 텍스트"에서 텍스트를 선택하여 요약, 번역, 용어설명을 실행하세요.
※ AI-Helper는 부적절한 답변을 할 수 있습니다.

선택된 텍스트

맨위로