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Volumn 252, Issue 10, 2012, Pages 5217-5234

On fractional Duhamel's principle and its applications

Author keywords

Cauchy problem; Distributed order differential operator equations; Fractional derivatives; Fractional Duhamel's principle; Inhomogeneous equation

Indexed keywords


EID: 84858291446     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2012.01.029     Document Type: Article
Times cited : (47)

References (41)
  • 1
    • 33644787625 scopus 로고    scopus 로고
    • A priori error estimates for upwind finite volume schemes in several space dimensions
    • Anh V.V., McVinish R. A priori error estimates for upwind finite volume schemes in several space dimensions. J. Appl. Math. Stoch. Anal. 2003, 16(2):97-117.
    • (2003) J. Appl. Math. Stoch. Anal. , vol.16 , Issue.2 , pp. 97-117
    • Anh, V.V.1    McVinish, R.2
  • 2
    • 0001311725 scopus 로고    scopus 로고
    • Stochastic solutions for fractional Cauchy problems
    • Baeumer B., Meerschaert M. Stochastic solutions for fractional Cauchy problems. Fract. Calc. Appl. Anal. 2001, 4:481-500.
    • (2001) Fract. Calc. Appl. Anal. , vol.4 , pp. 481-500
    • Baeumer, B.1    Meerschaert, M.2
  • 3
    • 84858296540 scopus 로고    scopus 로고
    • Fractional evolution equations in Banach spaces, Dissertation, Technische Universiteit Eindhoven
    • E. Bazhlekova, Fractional evolution equations in Banach spaces, Dissertation, Technische Universiteit Eindhoven, 2001.
    • (2001)
    • Bazhlekova, E.1
  • 5
    • 84977255207 scopus 로고
    • Linear models of dissipation whose Q is almost frequency independent. Part II
    • Caputo M. Linear models of dissipation whose Q is almost frequency independent. Part II. Geophys. J. R. Astr. Soc. 1967, 13:529-539.
    • (1967) Geophys. J. R. Astr. Soc. , vol.13 , pp. 529-539
    • Caputo, M.1
  • 6
    • 1942542248 scopus 로고    scopus 로고
    • Cauchy problem for fractional diffusion equations
    • Eidelman S.D., Kochubei A.N. Cauchy problem for fractional diffusion equations. J. Differential Equations 2004, 199:211-255.
    • (2004) J. Differential Equations , vol.199 , pp. 211-255
    • Eidelman, S.D.1    Kochubei, A.N.2
  • 7
    • 0038086852 scopus 로고
    • Fractional order evolution equations
    • El-Sayed A.M. Fractional order evolution equations. J. Fract. Calc. 1995, 7:89-100.
    • (1995) J. Fract. Calc. , vol.7 , pp. 89-100
    • El-Sayed, A.M.1
  • 9
    • 20444425307 scopus 로고
    • On a method of solving partial differential equations
    • Dubinskii Yu.A. On a method of solving partial differential equations. Sov. Math. Dokl. 1981, 23:583-587.
    • (1981) Sov. Math. Dokl. , vol.23 , pp. 583-587
    • Dubinskii, Y.1
  • 10
    • 84956260889 scopus 로고
    • The algebra of pseudo-differential operators with analytic symbols and its applications to mathematical physics
    • Dubinskii Yu.A. The algebra of pseudo-differential operators with analytic symbols and its applications to mathematical physics. Sov. Math. Surveys 1982, 37:107-153.
    • (1982) Sov. Math. Surveys , vol.37 , pp. 107-153
    • Dubinskii, Y.1
  • 11
    • 33747733181 scopus 로고
    • Sobolev spaces of infinite order
    • Dubinskii Yu.A. Sobolev spaces of infinite order. Russian Math. Surveys 1991, 46(6):97-131.
    • (1991) Russian Math. Surveys , vol.46 , Issue.6 , pp. 97-131
    • Dubinskii, Y.1
  • 12
    • 20144362710 scopus 로고    scopus 로고
    • Cauchy-type problem for an abstract differential equation with fractional derivatives
    • Glushak A.V. Cauchy-type problem for an abstract differential equation with fractional derivatives. Math. Notes 2005, 77(1):26-38.
    • (2005) Math. Notes , vol.77 , Issue.1 , pp. 26-38
    • Glushak, A.V.1
  • 13
    • 0001859547 scopus 로고
    • Abel Integral Equations: Analysis and Applications
    • Springer Verlag, Berlin
    • Gorenflo R., Vessella S. Abel Integral Equations: Analysis and Applications. Lecture Notes in Math. 1991, vol. 1461. Springer Verlag, Berlin.
    • (1991) Lecture Notes in Math. , vol.1461
    • Gorenflo, R.1    Vessella, S.2
  • 14
    • 32044462506 scopus 로고    scopus 로고
    • On the Cauchy and multi-point problems for partial pseudo-differential equations of fractional order
    • Gorenflo R., Luchko Yu.F., Umarov S.R. On the Cauchy and multi-point problems for partial pseudo-differential equations of fractional order. Fract. Calc. Appl. Anal. 2000, 3:249-275.
    • (2000) Fract. Calc. Appl. Anal. , vol.3 , pp. 249-275
    • Gorenflo, R.1    Luchko, Y.2    Umarov, S.R.3
  • 15
    • 4043104890 scopus 로고    scopus 로고
    • On solvability of linear fractional differential equations in Banach spaces
    • Gorenflo R., Luchko Yu.F., Zabreiko P.P. On solvability of linear fractional differential equations in Banach spaces. Fract. Calc. Appl. Anal. 1999, 2:163-176.
    • (1999) Fract. Calc. Appl. Anal. , vol.2 , pp. 163-176
    • Gorenflo, R.1    Luchko, Y.2    Zabreiko, P.P.3
  • 16
    • 80051610493 scopus 로고    scopus 로고
    • Fractional Fokker-Planck-Kolmogorov type equations and their associated stochastic differential equations
    • Hahn M., Umarov S. Fractional Fokker-Planck-Kolmogorov type equations and their associated stochastic differential equations. Fract. Calc. Appl. Anal. 2011, 14(1):56-80.
    • (2011) Fract. Calc. Appl. Anal. , vol.14 , Issue.1 , pp. 56-80
    • Hahn, M.1    Umarov, S.2
  • 17
    • 84856688304 scopus 로고    scopus 로고
    • SDEs driven by a time-changed Lévy process and their associated time-fractional pseudo-differential equations
    • Hahn M., Kobayashi K., Umarov S. SDEs driven by a time-changed Lévy process and their associated time-fractional pseudo-differential equations. J. Theoret. Probab. 2010, 10.1007/s10959-010-0289-4.
    • (2010) J. Theoret. Probab.
    • Hahn, M.1    Kobayashi, K.2    Umarov, S.3
  • 19
    • 0007045475 scopus 로고
    • A Cauchy problem for evolution equations of fractional order
    • Kochubei A.N. A Cauchy problem for evolution equations of fractional order. Differ. Equ. 1989, 25:967-974.
    • (1989) Differ. Equ. , vol.25 , pp. 967-974
    • Kochubei, A.N.1
  • 20
    • 37449011239 scopus 로고    scopus 로고
    • Distributed order calculus and equations of ultraslow diffusion
    • Kochubei A.N. Distributed order calculus and equations of ultraslow diffusion. J. Math. Anal. Appl. 2008, 340:252-281.
    • (2008) J. Math. Anal. Appl. , vol.340 , pp. 252-281
    • Kochubei, A.N.1
  • 21
    • 1942435440 scopus 로고
    • The Cauchy problem for an abstract differential equation with fractional derivatives
    • Kostin V.A. The Cauchy problem for an abstract differential equation with fractional derivatives. Russ. Dokl. Math. 1993, 46:316-319.
    • (1993) Russ. Dokl. Math. , vol.46 , pp. 316-319
    • Kostin, V.A.1
  • 24
    • 0036650957 scopus 로고    scopus 로고
    • Variable order and distributed order fractional operators
    • Lorenzo C.F., Hartley T.T. Variable order and distributed order fractional operators. Nonlinear Dynam. 2002, 29:57-98.
    • (2002) Nonlinear Dynam. , vol.29 , pp. 57-98
    • Lorenzo, C.F.1    Hartley, T.T.2
  • 26
    • 0002641421 scopus 로고    scopus 로고
    • The random walk's guide to anomalous diffusion: A fractional dynamics approach
    • Metzler R., Klafter J. The random walk's guide to anomalous diffusion: A fractional dynamics approach. Phys. Rep. 2000, 339:1-77.
    • (2000) Phys. Rep. , vol.339 , pp. 1-77
    • Metzler, R.1    Klafter, J.2
  • 31
    • 84858292723 scopus 로고    scopus 로고
    • Well-posedness of the Cauchy problem for inhomogeneous time-fractional pseudo-differential equations
    • Saydamatov E.M. Well-posedness of the Cauchy problem for inhomogeneous time-fractional pseudo-differential equations. Fract. Calc. Appl. Anal. 2006, 9(1):1-16.
    • (2006) Fract. Calc. Appl. Anal. , vol.9 , Issue.1 , pp. 1-16
    • Saydamatov, E.M.1
  • 32
    • 27144445120 scopus 로고    scopus 로고
    • Nonlocal boundary value problems for pseudo-differential and differential operator equations I
    • Umarov S.R. Nonlocal boundary value problems for pseudo-differential and differential operator equations I. Differ. Equ. 1997, 33:831-840.
    • (1997) Differ. Equ. , vol.33 , pp. 831-840
    • Umarov, S.R.1
  • 33
    • 27144554274 scopus 로고    scopus 로고
    • Nonlocal boundary value problems for pseudo-differential and differential operator equations II
    • Umarov S.R. Nonlocal boundary value problems for pseudo-differential and differential operator equations II. Differ. Equ. 1998, 34:374-381.
    • (1998) Differ. Equ. , vol.34 , pp. 374-381
    • Umarov, S.R.1
  • 34
    • 84858284101 scopus 로고
    • On well-posedness of boundary value problems for pseudo-differential equations with analytic symbols
    • Umarov S.R. On well-posedness of boundary value problems for pseudo-differential equations with analytic symbols. Russ. Dokl. Math. 1992, 45:229-233.
    • (1992) Russ. Dokl. Math. , vol.45 , pp. 229-233
    • Umarov, S.R.1
  • 35
    • 32044453310 scopus 로고    scopus 로고
    • Cauchy and nonlocal multi-point problems for distributed order pseudo-differential equations
    • Umarov S., Gorenflo R. Cauchy and nonlocal multi-point problems for distributed order pseudo-differential equations. Z. Anal. Anwend. 2005, 24:449-466.
    • (2005) Z. Anal. Anwend. , vol.24 , pp. 449-466
    • Umarov, S.1    Gorenflo, R.2
  • 36
    • 74349108984 scopus 로고    scopus 로고
    • A fractional analog of the Duhamel principle
    • Umarov S.R., Saydamatov E.M. A fractional analog of the Duhamel principle. Fract. Calc. Appl. Anal. 2006, 9(1):57-70.
    • (2006) Fract. Calc. Appl. Anal. , vol.9 , Issue.1 , pp. 57-70
    • Umarov, S.R.1    Saydamatov, E.M.2
  • 37
    • 33947374025 scopus 로고    scopus 로고
    • A generalization of the Duhamel principle for fractional order differential equations
    • English translation:
    • Umarov S.R., Saydamatov E.M. A generalization of the Duhamel principle for fractional order differential equations. Dokl. Ac. Sci. Russia. Dokl. Math. 2007, 75(1):94-96. English translation:.
    • (2007) Dokl. Ac. Sci. Russia. Dokl. Math. , vol.75 , Issue.1 , pp. 94-96
    • Umarov, S.R.1    Saydamatov, E.M.2
  • 38
    • 74349105778 scopus 로고    scopus 로고
    • Variable order differential equations with piecewise constant order-function and diffusion with changing modes
    • Umarov S., Steinberg S. Variable order differential equations with piecewise constant order-function and diffusion with changing modes. Z. Anal. Anwend. 2009, 28:431-450.
    • (2009) Z. Anal. Anwend. , vol.28 , pp. 431-450
    • Umarov, S.1    Steinberg, S.2
  • 39
    • 32044445069 scopus 로고
    • On the pseudo-differential operators with real analytic symbol and their applications
    • Van Tran Duc On the pseudo-differential operators with real analytic symbol and their applications. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 1989, 36:803-825.
    • (1989) J. Fac. Sci. Univ. Tokyo Sect. IA Math. , vol.36 , pp. 803-825
    • Van, T.D.1
  • 40
    • 0000637288 scopus 로고
    • Su un problema di Abel
    • Tonelli L. Su un problema di Abel. Math. Ann. 1928, 99:183-199.
    • (1928) Math. Ann. , vol.99 , pp. 183-199
    • Tonelli, L.1
  • 41
    • 33750050377 scopus 로고    scopus 로고
    • Differential equations in Banach spaces I. Theory of cosine operator functions II
    • Vasil'yev V.V., Piskarev S.I. Differential equations in Banach spaces I. Theory of cosine operator functions II. J. Math. Sci. 2004, 122(2):3055-3174.
    • (2004) J. Math. Sci. , vol.122 , Issue.2 , pp. 3055-3174
    • Vasil'yev, V.V.1    Piskarev, S.I.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.