메뉴 건너뛰기




Volumn 222, Issue 2, 2008, Pages 701-714

Similarity solutions to nonlinear heat conduction and Burgers/Korteweg-deVries fractional equations

Author keywords

Fractional Burgers Korteweg deVries equation; Fractional heat conduction equation; Lie group scaling transformation; Similarity solutions

Indexed keywords

DIFFERENCE EQUATIONS; DIFFERENTIAL EQUATIONS; DIFFERENTIATION (CALCULUS); HEAT CONDUCTION; LINEAR EQUATIONS; ORDINARY DIFFERENTIAL EQUATIONS; SEMICONDUCTOR DOPING;

EID: 53549087275     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2007.12.013     Document Type: Article
Times cited : (126)

References (24)
  • 2
    • 50949121966 scopus 로고    scopus 로고
    • An expansion formula for fractional derivatives and its applications
    • Atanackovic T.M., and Stankovic B. An expansion formula for fractional derivatives and its applications. Fract. Calculus Appl. Anal. 7 3 (2004) 365-378
    • (2004) Fract. Calculus Appl. Anal. , vol.7 , Issue.3 , pp. 365-378
    • Atanackovic, T.M.1    Stankovic, B.2
  • 4
    • 0039835768 scopus 로고    scopus 로고
    • Invariance of a partial differential equation of fractional order under the Lie group of scaling transformation
    • Buckwar E., and Luchko Y. Invariance of a partial differential equation of fractional order under the Lie group of scaling transformation. J. Math. Anal. Appl. 227 (1998) 81-97
    • (1998) J. Math. Anal. Appl. , vol.227 , pp. 81-97
    • Buckwar, E.1    Luchko, Y.2
  • 7
    • 51249167055 scopus 로고
    • Is the Fourier theory of heat propagation paradoxical
    • Fichera G. Is the Fourier theory of heat propagation paradoxical. Rend. Del Circolo Mat. Palermo 41 (1992) 5-28
    • (1992) Rend. Del Circolo Mat. Palermo , vol.41 , pp. 5-28
    • Fichera, G.1
  • 8
    • 0000103589 scopus 로고    scopus 로고
    • Wright functions as scale-invariant solutions of the diffusion-wave equation
    • Gorenflo R., Luchko Y., and Mainardi F. Wright functions as scale-invariant solutions of the diffusion-wave equation. J. Comput. Appl. Math. 118 (2000) 175-191
    • (2000) J. Comput. Appl. Math. , vol.118 , pp. 175-191
    • Gorenflo, R.1    Luchko, Y.2    Mainardi, F.3
  • 12
    • 0031448497 scopus 로고    scopus 로고
    • Seismic pulse propagation with constant Q and stable probability distribution
    • Mainardi F. Seismic pulse propagation with constant Q and stable probability distribution. Ann. Geofis. 40 (1997) 1311-1328
    • (1997) Ann. Geofis. , vol.40 , pp. 1311-1328
    • Mainardi, F.1
  • 14
    • 13444266285 scopus 로고    scopus 로고
    • Symmetry group analysis of Benney system and an application for shallow-water equations
    • Ozer T. Symmetry group analysis of Benney system and an application for shallow-water equations. Mech. Res. Comm. 32 (2005) 241-254
    • (2005) Mech. Res. Comm. , vol.32 , pp. 241-254
    • Ozer, T.1
  • 15
    • 4444320902 scopus 로고    scopus 로고
    • On symmetry group properties and general similarity forms of the Benney equations in the Lagrangian variables
    • Ozer T. On symmetry group properties and general similarity forms of the Benney equations in the Lagrangian variables. J. Comput. Appl. Math. 169 (2004) 297-313
    • (2004) J. Comput. Appl. Math. , vol.169 , pp. 297-313
    • Ozer, T.1
  • 17
    • 0022053193 scopus 로고
    • The general Lie group and similarity solutions for one-dimensional Vlasov-Maxwell equations
    • Roberts D. The general Lie group and similarity solutions for one-dimensional Vlasov-Maxwell equations. J. Plasma Phys. 33 (1985) 219-236
    • (1985) J. Plasma Phys. , vol.33 , pp. 219-236
    • Roberts, D.1
  • 18
    • 15544369500 scopus 로고    scopus 로고
    • Consistent modelling of infinite beams by fractional dynamics
    • Ruge P., and Trinks C. Consistent modelling of infinite beams by fractional dynamics. Nonlinear Dynam. 38 (2004) 267-284
    • (2004) Nonlinear Dynam. , vol.38 , pp. 267-284
    • Ruge, P.1    Trinks, C.2
  • 20
    • 0036869926 scopus 로고    scopus 로고
    • Treatment of Dynamic systems with fractional derivatives without evaluating memory-integrals
    • Trinks C., and Ruge P. Treatment of Dynamic systems with fractional derivatives without evaluating memory-integrals. Comput. Mech. 29 (2002) 471-476
    • (2002) Comput. Mech. , vol.29 , pp. 471-476
    • Trinks, C.1    Ruge, P.2
  • 23
    • 85031479830 scopus 로고    scopus 로고
    • L. Yuan, O.P. Agrawal, A numerical scheme for dynamic systems containing fractional derivatives, in: Proceedings of DETC'98 1998 ASME Design Engineering Technical Conferences, September 13-16, 1998, Atlanta Georgia
    • L. Yuan, O.P. Agrawal, A numerical scheme for dynamic systems containing fractional derivatives, in: Proceedings of DETC'98 1998 ASME Design Engineering Technical Conferences, September 13-16, 1998, Atlanta Georgia
  • 24
    • 0036554885 scopus 로고    scopus 로고
    • A numerical scheme for dynamic systems containing fractional derivatives
    • Yuan L., and Agrawal O.P. A numerical scheme for dynamic systems containing fractional derivatives. J. Vibration Acoustics 124 (2002) 321-324
    • (2002) J. Vibration Acoustics , vol.124 , pp. 321-324
    • Yuan, L.1    Agrawal, O.P.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.