메뉴 건너뛰기




Volumn 2010, Issue , 2010, Pages

On type of periodicity and Ergodicity to a class of fractional order differential equations

Author keywords

[No Author keywords available]

Indexed keywords


EID: 77951430590     PISSN: 16871839     EISSN: 16871847     Source Type: Journal    
DOI: 10.1155/2010/179750     Document Type: Article
Times cited : (81)

References (78)
  • 2
    • 0002847893 scopus 로고    scopus 로고
    • Fractional calculus: Integral and differential equations of fractional order
    • Vienna, Austria Springer CISM Courses and Lectures
    • Gorenflo R., Mainardi F., Carpinteri A., Mainardi F., Fractional calculus: integral and differential equations of fractional order Fractals and Fractional Calculus in Continuum Mechanics 1997 378 Vienna, Austria Springer 223 276 CISM Courses and Lectures
    • (1997) Fractals and Fractional Calculus in Continuum Mechanics , vol.378 , pp. 223-276
    • Gorenflo, R.1    Mainardi, F.2    Carpinteri, A.3    Mainardi, F.4
  • 4
    • 65049084387 scopus 로고    scopus 로고
    • Numerical detection of the lowest efficient dimensions for chaotic fractional differential systems
    • Hu T., Wang Y., Numerical detection of the lowest efficient dimensions for chaotic fractional differential systems Open Mathematics Journal 2008 1 11 18
    • (2008) Open Mathematics Journal , vol.1 , pp. 11-18
    • Hu, T.1    Wang, Y.2
  • 10
    • 1942542248 scopus 로고    scopus 로고
    • Cauchy problem for fractional diffusion equations
    • DOI 10.1016/j.jde.2003.12.002
    • Eidelman S. D., Kochubei A. N., Cauchy problem for fractional diffusion equations Journal of Differential Equations 2004 199 2 211 255 (Pubitemid 38516155)
    • (2004) Journal of Differential Equations , vol.199 , Issue.2 , pp. 211-255
    • Eidelman, S.D.1    Kochubei, A.N.2
  • 11
    • 34247154280 scopus 로고    scopus 로고
    • Global existence theory and chaos control of fractional differential equations
    • Lin W., Global existence theory and chaos control of fractional differential equations Journal of Mathematical Analysis and Applications 2007 332 1 709 726
    • (2007) Journal of Mathematical Analysis and Applications , vol.332 , Issue.1 , pp. 709-726
    • Lin, W.1
  • 14
    • 0036650890 scopus 로고    scopus 로고
    • Analogue realizations of fractional-order controllers. Fractional order calculus and its applications
    • Podlubny I., Petr I., Vinagre B. M., OLeary P., Dork L., Analogue realizations of fractional-order controllers. Fractional order calculus and its applications Nonlinear Dynamics 2002 29 14 281 296
    • (2002) Nonlinear Dynamics , vol.29 , Issue.14 , pp. 281-296
    • Podlubny, I.1    Petr, I.2    Vinagre, B.M.3    Oleary, P.4    Dork, L.5
  • 15
    • 0011628397 scopus 로고
    • Berlin, Germany Springer Lecture Notes in Mathematics, vol. 457
    • Ross B., Fractional Calculus and Its Applications 1975 Berlin, Germany Springer vi+381 Lecture Notes in Mathematics, vol. 457
    • (1975) Fractional Calculus and Its Applications , pp. 381
    • Ross, B.1
  • 17
    • 77949264980 scopus 로고    scopus 로고
    • A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions
    • Agarwal R. P., Benchohra M., Hamani S., A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions. to appear in Acta Applicandae Mathematicae
    • Acta Applicandae Mathematicae
    • Agarwal, R.P.1    Benchohra, M.2    Hamani, S.3
  • 18
    • 71549167605 scopus 로고    scopus 로고
    • Boundary value problems for fractional differential equations
    • Agarwal R. P., Benchohra M., Hamani S., Boundary value problems for fractional differential equations Georgian Mathematical Journal 2009 16 3 401 411
    • (2009) Georgian Mathematical Journal , vol.16 , Issue.3 , pp. 401-411
    • Agarwal, R.P.1    Benchohra, M.2    Hamani, S.3
  • 19
    • 67650110018 scopus 로고    scopus 로고
    • A survey on semilinear differential equations and inclusions involving Riemann-Liouville fractional derivative
    • Agarwal R. P., Belmekki M., Benchohra M., A survey on semilinear differential equations and inclusions involving Riemann-Liouville fractional derivative Advances in Difference Equations 2009 2009 47
    • (2009) Advances in Difference Equations , vol.2009 , pp. 47
    • Agarwal, R.P.1    Belmekki, M.2    Benchohra, M.3
  • 22
    • 37349014877 scopus 로고    scopus 로고
    • Theory of fractional differential inequalities and applications
    • Lakshmikantham V., Vatsala A. S., Theory of fractional differential inequalities and applications Communications in Applied Analysis 2007 11 3-4 395 402
    • (2007) Communications in Applied Analysis , vol.11 , Issue.34 , pp. 395-402
    • Lakshmikantham, V.1    Vatsala, A.S.2
  • 24
    • 0036680930 scopus 로고    scopus 로고
    • Some probability densities and fundamental solutions of fractional evolution equations
    • DOI 10.1016/S0960-0779(01)00208-9, PII S0960077901002089
    • El-Borai M. M., Some probability densities and fundamental solutions of fractional evolution equations Chaos, Solitons and Fractals 2002 14 3 433 440 (Pubitemid 34182465)
    • (2002) Chaos, Solitons and Fractals , vol.14 , Issue.3 , pp. 433-440
    • El-Borai, M.M.1
  • 25
    • 0345867025 scopus 로고    scopus 로고
    • Semigroups and some nonlinear fractional differential equations
    • El-Borai M. M., Semigroups and some nonlinear fractional differential equations Applied Mathematics and Computation 2004 149 3 823 831
    • (2004) Applied Mathematics and Computation , vol.149 , Issue.3 , pp. 823-831
    • El-Borai, M.M.1
  • 26
    • 34547561589 scopus 로고    scopus 로고
    • The fundamental solutions for fractional evolution equations of parabolic type
    • El-Borai M. M., The fundamental solutions for fractional evolution equations of parabolic type Journal of Applied Mathematics and Stochastic Analysis 2004 3 197 211
    • (2004) Journal of Applied Mathematics and Stochastic Analysis , Issue.3 , pp. 197-211
    • El-Borai, M.M.1
  • 28
    • 71549132795 scopus 로고    scopus 로고
    • Existence of the mild solution for some fractional differential equations with nonlocal conditions
    • Mophou G. M., NGurkata G. M., Existence of the mild solution for some fractional differential equations with nonlocal conditions Semigroup Forum 2009 79 2 315 322
    • (2009) Semigroup Forum , vol.79 , Issue.2 , pp. 315-322
    • Mophou, G.M.1    Ngurkata, G.M.2
  • 29
    • 58149231350 scopus 로고    scopus 로고
    • A Cauchy problem for some fractional abstract differential equation with non local conditions
    • NGurkata G. M., A Cauchy problem for some fractional abstract differential equation with non local conditions Nonlinear Analysis: Theory, Methods Applications 2009 70 5 1873 1876
    • (2009) Nonlinear Analysis: Theory, Methods Applications , vol.70 , Issue.5 , pp. 1873-1876
    • Ngurkata, G.M.1
  • 31
    • 58149196822 scopus 로고    scopus 로고
    • Existence results for fractional functional differential inclusions with infinite delay and applications to control theory
    • Benchohra M., Henderson J., Ntouyas S. K., Ouahab A., Existence results for fractional functional differential inclusions with infinite delay and applications to control theory Fractional Calculus Applied Analysis 2008 11 1 35 56
    • (2008) Fractional Calculus Applied Analysis , vol.11 , Issue.1 , pp. 35-56
    • Benchohra, M.1    Henderson, J.2    Ntouyas, S.K.3    Ouahab, A.4
  • 33
    • 53949105887 scopus 로고    scopus 로고
    • Some results for fractional boundary value problem of differential inclusions
    • Ouahab A., Some results for fractional boundary value problem of differential inclusions Nonlinear Analysis: Theory, Methods Applications 2008 69 11 3877 3896
    • (2008) Nonlinear Analysis: Theory, Methods Applications , vol.69 , Issue.11 , pp. 3877-3896
    • Ouahab, A.1
  • 34
    • 53249152135 scopus 로고    scopus 로고
    • Almost automorphic solutions to a class of semilinear fractional differential equations
    • Cuevas C., Lizama C., Almost automorphic solutions to a class of semilinear fractional differential equations Applied Mathematics Letters 2008 21 12 1315 1319
    • (2008) Applied Mathematics Letters , vol.21 , Issue.12 , pp. 1315-1319
    • Cuevas, C.1    Lizama, C.2
  • 35
    • 76349114928 scopus 로고    scopus 로고
    • Almost automorphic solutions to integral equations on the line
    • Cuevas C., Lizama C., Almost automorphic solutions to integral equations on the line Semigroup Forum 2009 79 3 461 472
    • (2009) Semigroup Forum , vol.79 , Issue.3 , pp. 461-472
    • Cuevas, C.1    Lizama, C.2
  • 36
    • 0000743990 scopus 로고
    • Pseudo-almost-periodic solutions of some differential equations
    • Zhang C. Y., Pseudo-almost-periodic solutions of some differential equations Journal of Mathematical Analysis and Applications 1994 181 1 62 76
    • (1994) Journal of Mathematical Analysis and Applications , vol.181 , Issue.1 , pp. 62-76
    • Zhang, C.Y.1
  • 37
    • 84966211078 scopus 로고
    • Integration of vector-valued pseudo-almost periodic functions
    • Zhang C. Y., Integration of vector-valued pseudo-almost periodic functions Proceedings of the American Mathematical Society 1994 121 1 167 174
    • (1994) Proceedings of the American Mathematical Society , vol.121 , Issue.1 , pp. 167-174
    • Zhang, C.Y.1
  • 38
    • 0000479945 scopus 로고
    • Pseudo almost periodic solutions of some differential equations. II
    • Zhang C. Y., Pseudo almost periodic solutions of some differential equations. II Journal of Mathematical Analysis and Applications 1995 192 2 543 561
    • (1995) Journal of Mathematical Analysis and Applications , vol.192 , Issue.2 , pp. 543-561
    • Zhang, C.Y.1
  • 40
    • 0030216446 scopus 로고    scopus 로고
    • Exponential dichotomy and existence of pseudo almost-periodic solutions of some differential equations
    • Ait Dads E., Arino O., Exponential dichotomy and existence of pseudo almost-periodic solutions of some differential equations Nonlinear Analysis: Theory, Methods Applications 1996 27 4 369 386
    • (1996) Nonlinear Analysis: Theory, Methods Applications , vol.27 , Issue.4 , pp. 369-386
    • Ait Dads, E.1    Arino, O.2
  • 41
    • 0031126756 scopus 로고    scopus 로고
    • Pseudo almost periodic solutions for some differential equations in a Banach space
    • Ait Dads E., Ezzinbi K., Arino O., Pseudo almost periodic solutions for some differential equations in a Banach space Nonlinear Analysis: Theory, Methods Applications 1997 28 7 1141 1155 (Pubitemid 127423115)
    • (1997) Nonlinear Analysis, Theory, Methods and Applications , vol.28 , Issue.7 , pp. 1141-1155
    • Ait Dads, E.1    Ezzinbi, K.2    Arino, O.3
  • 42
    • 0006795644 scopus 로고    scopus 로고
    • Composition of pseudo-almost periodic functions and Cauchy problems with operator of nondense domain
    • Amir B., Maniar L., Composition of pseudo-almost periodic functions and Cauchy problems with operator of nondense domain Annales Mathmatiques Blaise Pascal 1999 6 1 1 11
    • (1999) Annales Mathmatiques Blaise Pascal , vol.6 , Issue.1 , pp. 1-11
    • Amir, B.1    Maniar, L.2
  • 43
    • 61349156728 scopus 로고    scopus 로고
    • Pseudo-almost periodic solutions for abstract partial functional differential equations
    • Cuevas C., Hernndez M. E., Pseudo-almost periodic solutions for abstract partial functional differential equations Applied Mathematics Letters 2009 22 4 534 538
    • (2009) Applied Mathematics Letters , vol.22 , Issue.4 , pp. 534-538
    • Cuevas, C.1    Hernndez, M.E.2
  • 44
    • 0035400758 scopus 로고    scopus 로고
    • Existence and uniqueness of pseudo almost periodic solutions of semilinear Cauchy problems with non dense domain
    • DOI 10.1016/S0362-546X(99)00330-2, PII S0362546X99003302
    • Cuevas C., Pinto M., Existence and uniqueness of pseudo almost periodic solutions of semilinear Cauchy problems with non dense domain Nonlinear Analysis: Theory, Methods Applications 2001 45 1 73 83 (Pubitemid 32427144)
    • (2001) Nonlinear Analysis, Theory, Methods and Applications , vol.45 , Issue.1 , pp. 73-83
    • Cuevas, C.1    Pinto, M.2
  • 45
    • 12244256136 scopus 로고    scopus 로고
    • Pseudo almost periodic solutions to some differential equations
    • DOI 10.1016/j.na.2004.11.002, PII S0362546X0400519X
    • Diagana T., Pseudo almost periodic solutions to some differential equations Nonlinear Analysis: Theory, Methods Applications 2005 60 7 1277 1286 (Pubitemid 40114277)
    • (2005) Nonlinear Analysis, Theory, Methods and Applications , vol.60 , Issue.7 , pp. 1277-1286
    • Diagana, T.1
  • 46
    • 33644533845 scopus 로고    scopus 로고
    • Pseudo-almost-periodic solutions to some semilinear differential equations
    • DOI 10.1016/j.mcm.2005.04.013, PII S0895717705004553
    • Diagana T., Mahop C. M., NGurkata G. M., Pseudo-almost-periodic solutions to some semilinear differential equations Mathematical and Computer Modelling 2006 43 1-2 89 96 (Pubitemid 43294571)
    • (2006) Mathematical and Computer Modelling , vol.43 , Issue.1-2 , pp. 89-96
    • Diagana, T.1    Mahop, C.M.2    N'Guerekata, G.M.3
  • 47
    • 33644962661 scopus 로고    scopus 로고
    • Existence and uniqueness of pseudo-almost periodic solutions to some classes of semilinear differential equations and applications
    • Diagana T., Mahop C. M., NGurkata G. M., Toni B., Existence and uniqueness of pseudo-almost periodic solutions to some classes of semilinear differential equations and applications Nonlinear Analysis: Theory, Methods Applications 2006 64 11 2442 2453
    • (2006) Nonlinear Analysis: Theory, Methods Applications , vol.64 , Issue.11 , pp. 2442-2453
    • Diagana, T.1    Mahop, C.M.2    Ngurkata, G.M.3    Toni, B.4
  • 48
    • 77951467584 scopus 로고    scopus 로고
    • Pseudo almost periodic solutions to a neutral delay integral equation
    • Diagana T., Mahop C. M., Pseudo almost periodic solutions to a neutral delay integral equation Cubo 2007 9 1 47 55
    • (2007) Cubo , vol.9 , Issue.1 , pp. 47-55
    • Diagana, T.1    Mahop, C.M.2
  • 49
    • 33846820533 scopus 로고    scopus 로고
    • Existence of pseudo almost periodic solutions to some classes of partial hyperbolic evolution equations
    • Diagana T., Existence of pseudo almost periodic solutions to some classes of partial hyperbolic evolution equations Electronic Journal of Qualitative Theory of Differential Equations 2007 3 12
    • (2007) Electronic Journal of Qualitative Theory of Differential Equations , Issue.3 , pp. 12
    • Diagana, T.1
  • 50
    • 67349236203 scopus 로고    scopus 로고
    • S -asymptotically -periodic solutions of semilinear fractional integro-differential equations
    • Cuevas C., de Souza J. C., S -asymptotically -periodic solutions of semilinear fractional integro-differential equations Applied Mathematics Letters 2009 22 6 865 870
    • (2009) Applied Mathematics Letters , vol.22 , Issue.6 , pp. 865-870
    • Cuevas, C.1    De Souza, J.C.2
  • 51
    • 71849104604 scopus 로고    scopus 로고
    • Existence of S -asymptotically -periodic solutions for fractional order functional integro-differential equations with infinite delay
    • Cuevas C., de Souza J. C., Existence of S -asymptotically -periodic solutions for fractional order functional integro-differential equations with infinite delay Nonlinear Analysis: Theory, Methods Applications 2010 72 3-4 1683 1689
    • (2010) Nonlinear Analysis: Theory, Methods Applications , vol.72 , Issue.34 , pp. 1683-1689
    • Cuevas, C.1    De Souza, J.C.2
  • 52
    • 33749339663 scopus 로고    scopus 로고
    • Basel, Switzerland Birkhuser Operator Theory: Advances and Applications
    • Haase M., The Functional Calculus for Sectorial Operators 2006 169 Basel, Switzerland Birkhuser xiv+392 Operator Theory: Advances and Applications
    • (2006) The Functional Calculus for Sectorial Operators , vol.169 , pp. 392
    • Haase, M.1
  • 53
    • 53249107043 scopus 로고    scopus 로고
    • Asymptotic behaviour of the solutions of fractional integro-differential equations and some time discretizations
    • Cuesta E., Asymptotic behaviour of the solutions of fractional integro-differential equations and some time discretizations Discrete and Continuous Dynamical Systems 2007 277 285
    • (2007) Discrete and Continuous Dynamical Systems , pp. 277-285
    • Cuesta, E.1
  • 58
    • 0038624590 scopus 로고    scopus 로고
    • On approximation and representation of k -regularized resolvent families
    • Lizama C., On approximation and representation of k -regularized resolvent families Integral Equations and Operator Theory 2001 41 2 223 229
    • (2001) Integral Equations and Operator Theory , vol.41 , Issue.2 , pp. 223-229
    • Lizama, C.1
  • 59
    • 0038392424 scopus 로고    scopus 로고
    • Rates of approximation and ergodic limits of regularized operator families
    • Lizama C., Prado H., Rates of approximation and ergodic limits of regularized operator families Journal of Approximation Theory 2003 122 1 42 61
    • (2003) Journal of Approximation Theory , vol.122 , Issue.1 , pp. 42-61
    • Lizama, C.1    Prado, H.2
  • 60
    • 19044391698 scopus 로고    scopus 로고
    • On perturbation of k -regularized resolvent families
    • Lizama C., Snchez J., On perturbation of k -regularized resolvent families Taiwanese Journal of Mathematics 2003 7 2 217 227
    • (2003) Taiwanese Journal of Mathematics , vol.7 , Issue.2 , pp. 217-227
    • Lizama, C.1    Snchez, J.2
  • 61
    • 34250194945 scopus 로고    scopus 로고
    • Asymptotic behavior of (a,k) -regularized resolvent families at zero
    • Shaw S.-Y., Chen J.-C., Asymptotic behavior of (a,k) -regularized resolvent families at zero Taiwanese Journal of Mathematics 2006 10 2 531 542
    • (2006) Taiwanese Journal of Mathematics , vol.10 , Issue.2 , pp. 531-542
    • Shaw, S.-Y.1    Chen, J.-C.2
  • 62
  • 63
    • 0003451928 scopus 로고
    • Berlin, Germany Springer Lecture Notes in Mathematics, vol. 377
    • Fink A. M., Almost Periodic Differential Equations 1974 Berlin, Germany Springer viii+336 Lecture Notes in Mathematics, vol. 377
    • (1974) Almost Periodic Differential Equations , pp. 336
    • Fink, A.M.1
  • 65
    • 0035869881 scopus 로고    scopus 로고
    • Composition of pseudo almost-periodic functions and semilinear differential equations
    • Li H.-X., Huang F.-L., Li J.-Y., Composition of pseudo almost-periodic functions and semilinear differential equations Journal of Mathematical Analysis and Applications 2001 255 2 436 446
    • (2001) Journal of Mathematical Analysis and Applications , vol.255 , Issue.2 , pp. 436-446
    • Li, H.-X.1    Huang, F.-L.2    Li, J.-Y.3
  • 66
    • 72149112210 scopus 로고    scopus 로고
    • Compact almost automorphic solutions to integral equations with infinite delay
    • Henrquez H. R., Lizama C., Compact almost automorphic solutions to integral equations with infinite delay Nonlinear Analysis: Theory, Methods Applications 2009 71 12 6029 6037
    • (2009) Nonlinear Analysis: Theory, Methods Applications , vol.71 , Issue.12 , pp. 6029-6037
    • Henrquez, H.R.1    Lizama, C.2
  • 71
    • 9244237996 scopus 로고
    • Quelques remarques sur les fonctions asymptotiquement presque automorphes
    • NGurkata G. M., Quelques remarques sur les fonctions asymptotiquement presque automorphes Les Annales des Sciences Mathmatiques du Qubec 1983 7 2 185 191
    • (1983) Les Annales des Sciences Mathmatiques du Qubec , vol.7 , Issue.2 , pp. 185-191
    • Ngurkata, G.M.1
  • 72
    • 9244234347 scopus 로고    scopus 로고
    • On the topological structure of almost automorphic and asymptotically almost automorphic solutions of differential and integral equations in abstract spaces
    • Bugajewski D., NGurkata G. M., On the topological structure of almost automorphic and asymptotically almost automorphic solutions of differential and integral equations in abstract spaces Nonlinear Analysis: Theory, Methods Applications 2004 59 8 1333 1345
    • (2004) Nonlinear Analysis: Theory, Methods Applications , vol.59 , Issue.8 , pp. 1333-1345
    • Bugajewski, D.1    Ngurkata, G.M.2
  • 73
    • 33751210326 scopus 로고    scopus 로고
    • Almost automorphic solutions to some classes of partial evolution equations
    • DOI 10.1016/j.aml.2006.05.015, PII S0893965906001996
    • Diagana T., NGurkata G. M., Almost automorphic solutions to some classes of partial evolution equations Applied Mathematics Letters 2007 20 4 462 466 (Pubitemid 44792893)
    • (2007) Applied Mathematics Letters , vol.20 , Issue.4 , pp. 462-466
    • Diagana, T.1    N'Guerekata, G.M.2
  • 74
    • 7244239595 scopus 로고    scopus 로고
    • Almost automorphic solutions of evolution equations
    • DOI 10.1090/S0002-9939-04-07571-9, PII S0002993904075719
    • Diagana T., NGurkata G. M., Minh N. V., Almost automorphic solutions of evolution equations Proceedings of the American Mathematical Society 2004 132 11 3289 3298 (Pubitemid 39443479)
    • (2004) Proceedings of the American Mathematical Society , vol.132 , Issue.11 , pp. 3289-3298
    • Diagana, T.1    Nguerekata, G.2    Van Minh, N.3
  • 75
    • 34548847768 scopus 로고    scopus 로고
    • Asymptotically almost automorphic solutions for some integrodifferential equations with nonlocal initial conditions
    • Ding H.-S., Xiao T.-J., Liang J., Asymptotically almost automorphic solutions for some integrodifferential equations with nonlocal initial conditions Journal of Mathematical Analysis and Applications 2008 338 1 141 151
    • (2008) Journal of Mathematical Analysis and Applications , vol.338 , Issue.1 , pp. 141-151
    • Ding, H.-S.1    Xiao, T.-J.2    Liang, J.3
  • 76
    • 64849090450 scopus 로고    scopus 로고
    • Existence of asymptotically almost automorphic solutions to some abstract partial neutral integro-differential equations
    • Diagana T., Hernndez E. M., dos Santos J. P. C., Existence of asymptotically almost automorphic solutions to some abstract partial neutral integro-differential equations Nonlinear Analysis: Theory, Methods Applications 2009 71 1-2 248 257
    • (2009) Nonlinear Analysis: Theory, Methods Applications , vol.71 , Issue.12 , pp. 248-257
    • Diagana, T.1    Hernndez, E.M.2    Dos Santos, J.P.C.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.