메뉴 건너뛰기




Volumn 17, Issue 1, 2010, Pages 31-47

Pseudo-almost automorphic solutions to a class of semilinear fractional differential equations

Author keywords

Mild solutions; Pseudo almost automorphic function; Semilinear fractional equations; Solution operator

Indexed keywords


EID: 77949522096     PISSN: 1074133X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (21)

References (45)
  • 3
    • 67650110018 scopus 로고    scopus 로고
    • A survey on semilinear differential equations and inclusions involving Riemann-Liouville fractional derivative
    • Article ID 981728 doi:10.1155/2009/981728
    • R. P. Agarwal, M. Belmekki, and M. Benchohra, A survey on semilinear differential equations and inclusions involving Riemann-Liouville fractional derivative, Adv. Difference Equ., Vol. 2009, Article ID 981728, 47 pages, doi:10.1155/2009/981728.
    • Adv. Difference Equ. , vol.2009 , pp. 47
    • Agarwal, R.P.1    Belmekki, M.2    Benchohra, M.3
  • 4
    • 77949264980 scopus 로고    scopus 로고
    • A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions
    • doi: 10.1007/sl 10440-008-9356-9366
    • R. P. Agarwal, M. Benchohra, and S. Hamani, A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions, Acta Appl. Math, doi: 10.1007/sl 10440-008-9356-9366
    • Acta Appl. Math
    • Agarwal, R.P.1    Benchohra, M.2    Hamani, S.3
  • 5
    • 54149085799 scopus 로고    scopus 로고
    • Weighted pseudo almost periodic solutions to some partial neutral functional differential equations
    • R. P. Agarwal, T. Diagana, and E. Hernandez, Weighted pseudo almost periodic solutions to some partial neutral functional differential equations. J. Nonlinear Convex Anal. 8 (3) (2007), 397-415.
    • (2007) J. Nonlinear Convex Anal. , vol.8 , Issue.3 , pp. 397-415
    • Agarwal, R.P.1    Diagana, T.2    Hernandez, E.3
  • 8
    • 33644787625 scopus 로고    scopus 로고
    • Fractional differential equations driven by Levy noise
    • V.V. Ahn, and R. Mcvinish, Fractional differential equations driven by Levy noise. J. Appl. Stock Anal. 16 (2) (2003), 97-119.
    • (2003) J. Appl. Stock Anal. , vol.16 , Issue.2 , pp. 97-119
    • Ahn, V.V.1    Mcvinish, R.2
  • 9
    • 68949117892 scopus 로고    scopus 로고
    • Almost automorphic and pseudo almost automorphic solutions to semilinear evolution equations with non dense domain
    • Article ID 298207 doi 10.1155/2009/298207
    • B. de Andrade, and C. Cuevas, Almost automorphic and pseudo almost automorphic solutions to semilinear evolution equations with non dense domain, Journal of Inequalities and Applications, 2009 (2009), Article ID 298207,8 pages, doi 10.1155/2009/298207.
    • (2009) Journal of Inequalities and Applications , vol.2009 , pp. 8
    • De Andrade, B.1    Cuevas, C.2
  • 10
    • 70449524307 scopus 로고    scopus 로고
    • Compact almost automorphic solutions to semilinear Cauchy problems with nondense domain
    • B. de Andrade, and C. Cuevas , Compact almost automorphic solutions to semilinear Cauchy problems with nondense domain, Applied Mathematics and Computation 215 (2009), 2843-2849.
    • (2009) Applied Mathematics and Computation , vol.215 , pp. 2843-2849
    • De Andrade, B.1    Cuevas, C.2
  • 11
    • 73249139305 scopus 로고    scopus 로고
    • S-asymptotically ω-periodic and asymptotically ωperiodic solutions to semilinear Cauchy problems with non dense domain
    • to appear
    • B. de Andrade, and C. Cuevas , S-asymptotically ω-periodic and asymptotically ωperiodic solutions to semilinear Cauchy problems with non dense domain, Nonlinear Analysis Series A: Theory, Methods and Applications, 2009, to appear.
    • (2009) Nonlinear Analysis Series A: Theory, Methods and Applications
    • De Andrade, B.1    Cuevas, C.2
  • 12
    • 53949107192 scopus 로고    scopus 로고
    • Almost automorphic mild solutions to fractional differential equations
    • D. Araya, and C. Lizama, Almost automorphic mild solutions to fractional differential equations. Nonlinear Analysis 69 (11) (2008), 3692-3705.
    • (2008) Nonlinear Analysis , vol.69 , Issue.11 , pp. 3692-3705
    • Araya, D.1    Lizama, C.2
  • 14
    • 33845354119 scopus 로고    scopus 로고
    • 0-semigroups and solutions of linear and semilinear abstract differential equations
    • 0-semigroups and solutions of linear and semilinear abstract differential equations, Russ. J. Math. Phys. 13 (1) (2006), 13-30.
    • (2006) Russ. J. Math. Phys. , vol.13 , Issue.1 , pp. 13-30
    • Basit, B.1    Pryde, A.J.2
  • 16
    • 77956929181 scopus 로고    scopus 로고
    • S-asymptotically ω-periodic solutions of abstract partial neutral integro-differential equations
    • to appear
    • A. Caicedo, and C. Cuevas, S-asymptotically ω-periodic solutions of abstract partial neutral integro-differential equations, Functional Differential Equations 17 ( 1-2), 2010, to appear.
    • Functional Differential Equations , vol.17 , Issue.1-2 , pp. 2010
    • Caicedo, A.1    Cuevas, C.2
  • 17
    • 53249107043 scopus 로고    scopus 로고
    • Asymptotic behaviour of the solutions of fractional integro-differential equations and some time discretizations
    • E. Cuesta, Asymptotic behaviour of the solutions of fractional integro-differential equations and some time discretizations, Discrete Contin. Dyn. Syst. (Supplement) (2007), 277-285.
    • (2007) Discrete Contin. Dyn. Syst. (Supplement) , pp. 277-285
    • Cuesta, E.1
  • 18
    • 0035400758 scopus 로고    scopus 로고
    • Existence and uniqueness of pseudo-almost periodic solutions of semilinear Cauchy problems with non dense domain
    • C. Cuevas; M. Pinto, Existence and uniqueness of pseudo-almost periodic solutions of semilinear Cauchy problems with non dense domain. Nonlinear Anal 45 (2001), no.1, 73-83.
    • (2001) Nonlinear Anal , vol.45 , Issue.1 , pp. 73-83
    • Cuevas, C.1    Pinto, M.2
  • 19
    • 61349156728 scopus 로고    scopus 로고
    • Pseudo-almost periodic solutions for abstract partial functional differential equations
    • C. Cuevas, and E. Hernández, Pseudo-almost periodic solutions for abstract partial functional differential equations, Applied Mathematics Letters 22 (2009), 534-538.
    • (2009) Applied Mathematics Letters , vol.22 , pp. 534-538
    • Cuevas, C.1    Hernández, E.2
  • 20
    • 53249152135 scopus 로고    scopus 로고
    • Almost automorphic solutions to a class of semilinear fractional differential equations
    • C. Cuevas, and C. Lizama, Almost automorphic solutions to a class of semilinear fractional differential equations, Applied Mathematics Letters 21 ( 2008), 1315-1319.
    • (2008) Applied Mathematics Letters , vol.21 , pp. 1315-1319
    • Cuevas, C.1    Lizama, C.2
  • 21
    • 67349236203 scopus 로고    scopus 로고
    • S-Asymptotically ω-periodic solutions of semilinear fractional Integro-Differential Equations
    • C. Cuevas, and J. C. de Souza, S-Asymptotically ω-periodic solutions of semilinear fractional Integro-Differential Equations, Applied Mathematics Letters 22 (2009), 865-870.
    • (2009) Applied Mathematics Letters , vol.22 , pp. 865-870
    • Cuevas, C.1    De Souza, J.C.2
  • 22
    • 71849104604 scopus 로고    scopus 로고
    • Existence of S-asymptotically ω-periodic solutions for fractional order functional Integro-Differential Equations with infinite delay
    • C. Cuevas, and J.C. de Souza, Existence of S-asymptotically ω-periodic solutions for fractional order functional Integro-Differential Equations with infinite delay, Nonlinear Anal. 72 (2010), 1683-1689.
    • (2010) Nonlinear Anal. , vol.72 , pp. 1683-1689
    • Cuevas, C.1    De Souza, J.C.2
  • 23
    • 76349114928 scopus 로고    scopus 로고
    • Almost automorphic solutions to integral equations on the line
    • C. Cuevas, and C. Lizama, Almost automorphic solutions to integral equations on the line, Semigroup Forum 79 (2009), 461-472.
    • (2009) Semigroup Forum , vol.79 , pp. 461-472
    • Cuevas, C.1    Lizama, C.2
  • 24
    • 1942542248 scopus 로고    scopus 로고
    • Cauchy problem for fractional diffusion equations
    • S.D. Eidelman, and A.N. Kochubei, Cauchy problem for fractional diffusion equations. J. of Differential Equations 199 (2004), 211-255.
    • (2004) J. of Differential Equations , vol.199 , pp. 211-255
    • Eidelman, S.D.1    Kochubei, A.N.2
  • 25
    • 0003369059 scopus 로고
    • Second Order Linear Differential equations in Banach spaces
    • Amsterdam-New York-Oxford: North-Holland
    • H.O Fattorini, Second Order Linear Differential equations in Banach spaces. NorthHolland Math. Studies, 108. Amsterdam-New York-Oxford: North-Holland, 1985.
    • (1985) NorthHolland Math. Studies , vol.108
    • Fattorini, H.O.1
  • 26
    • 0037443357 scopus 로고    scopus 로고
    • On the existence and uniqueness of almost periodic solutions for delay logistic equations
    • C. Feng, On the existence and uniqueness of almost periodic solutions for delay logistic equations, Appl Math. Comput. 136 (2-3) (2003), 487-494.
    • (2003) Appl Math. Comput. , vol.136 , Issue.2-3 , pp. 487-494
    • Feng, C.1
  • 27
    • 0002847893 scopus 로고    scopus 로고
    • Fractional calculus: Integral and differential equations of fractional order
    • A. Carpinteri, and F. Mainardi (Editors) Springer-Verlag, Vienna, New York
    • R. Gorenflo, and F. Mainardi, Fractional Calculus: Integral and Differential Equations of Fractional Order, A. Carpinteri, and F. Mainardi (Editors): Fractals and Fractional Calculus in Continuum Mechanics, Springer-Verlag, Vienna, New York, 1997, 223-276.
    • (1997) Fractals and Fractional Calculus in Continuum Mechanics , pp. 223-276
    • Gorenflo, R.1    Mainardi, F.2
  • 29
    • 41949103912 scopus 로고
    • Asymptotically almost periodic solutions of differential equations
    • R. C. Grimmer, Asymptotically almost periodic solutions of differential equations, SIAM J. Appl Math. 17 (1969), 109-115.
    • (1969) SIAM J. Appl Math. , vol.17 , pp. 109-115
    • Grimmer, R.C.1
  • 31
    • 38049089402 scopus 로고    scopus 로고
    • Composition of pseudo almost automorphic functions
    • J. Liang, J. Zhang, and T.J. Xiao, Composition of pseudo almost automorphic functions, J. Math. Anal. Appl. 340 (2008) 1493-1499.
    • (2008) J. Math. Anal. Appl. , vol.340 , pp. 1493-1499
    • Liang, J.1    Zhang, J.2    Xiao, T.J.3
  • 33
    • 72149112210 scopus 로고    scopus 로고
    • Compact Almost Automorphic Solutions to Integral equations with infinite delay
    • doi 10.1016/j.na. 2009.05.042
    • H. Henrfquez, and C. Lizama, Compact Almost Automorphic Solutions to Integral equations with infinite delay, Nonlinear Analysis (2009), doi 10.1016/j.na. 2009.05.042.
    • (2009) Nonlinear Analysis
    • Henrfquez, H.1    Lizama, C.2
  • 35
    • 84968468465 scopus 로고
    • Asymptotically periodic solutions of a class of second order nonlinear differential equations
    • Z. C. Liang, Asymptotically periodic solutions of a class of second order nonlinear differential equations, Proc. Amer. Math. Soc. 99 (4) (1987), 693-699.
    • (1987) Proc. Amer. Math. Soc. , vol.99 , Issue.4 , pp. 693-699
    • Liang, Z.C.1
  • 36
    • 0034652891 scopus 로고    scopus 로고
    • Regularized solutions for abstract Volterra equations
    • C. Lizama, Regularized solutions for abstract Volterra equations, J. Math. Anal. Appl. 243 (2000), 278-292.
    • (2000) J. Math. Anal. Appl. , vol.243 , pp. 278-292
    • Lizama, C.1
  • 39
    • 42249086144 scopus 로고    scopus 로고
    • Pseudo almost automorphic solutions to semilinear differential equations in Banach space
    • T.J. Xiao, J. Liang, and J. Zhang, Pseudo almost automorphic solutions to semilinear differential equations in Banach space, Semigroup Forum 76 (2008), 518-524.
    • (2008) Semigroup Forum , vol.76 , pp. 518-524
    • Xiao, T.J.1    Liang, J.2    Zhang, J.3
  • 40
    • 62949148699 scopus 로고    scopus 로고
    • Pseudo almost automorphic mild solutions to nonautonomous differential equations and applications
    • doi 10.1016/j.na.2008.08.018
    • T.J. Xiao, J. Liang, and J. Zhang, Pseudo almost automorphic mild solutions to nonautonomous differential equations and applications, Nonlinear Anal. (2008), doi 10.1016/j.na.2008.08.018.
    • (2008) Nonlinear Anal.
    • Xiao, T.J.1    Liang, J.2    Zhang, J.3
  • 41
    • 84966253390 scopus 로고
    • Asymptotic almost periodicity of solutions of a system of differential equations
    • W. R. Utz, and P.Waltman, Asymptotic almost periodicity of solutions of a system of differential equations, Proc. Amer. Math. Soc. 18 (1967), 597-601.
    • (1967) Proc. Amer. Math. Soc. , vol.18 , pp. 597-601
    • Utz, W.R.1    Waltman, P.2
  • 42
    • 33750800862 scopus 로고    scopus 로고
    • Global stability and asymptotically periodic solutions for nonautonomous cooperative Lotka-Volterra diffusion system
    • F. Wei, and K. Wang, Global stability and asymptotically periodic solutions for nonautonomous cooperative Lotka-Volterra diffusion system, Applied Math, and Computation 182 (2006), 161-165.
    • (2006) Applied Math, and Computation , vol.182 , pp. 161-165
    • Wei, F.1    Wang, K.2
  • 43
    • 33646135560 scopus 로고    scopus 로고
    • Asymptoticaly periodic solutions of N-species cooperation system with time delay
    • F. Wei, and K. Wang, Asymptoticaly periodic solutions of N-species cooperation system with time delay, Nonlinear Analysis: Real World and Applications 7 (2006), 591-596.
    • (2006) Nonlinear Analysis: Real World and Applications , vol.7 , pp. 591-596
    • Wei, F.1    Wang, K.2
  • 45
    • 3042800316 scopus 로고    scopus 로고
    • Existence and global attractivity of almost periodic solutions for cellular neutral network with distributed delays
    • H. Zhao, Existence and global attractivity of almost periodic solutions for cellular neutral network with distributed delays, Appl. Math. Comput. 154 (3) (2004), 683-695.
    • (2004) Appl. Math. Comput. , vol.154 , Issue.3 , pp. 683-695
    • Zhao, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.