메뉴 건너뛰기




Volumn 71, Issue 11, 2009, Pages 5551-5559

Existence and uniqueness of mild solutions to a semilinear integrodifferential equation of fractional order

Author keywords

Existence and uniqueness; Fixed point; Fractional differential equation; Nonlocal initial conditions

Indexed keywords

ANALYTIC SEMIGROUP; EXISTENCE AND UNIQUENESS; FIXED POINT; FRACTIONAL DIFFERENTIAL EQUATION; FRACTIONAL ORDER; MILD SOLUTION; NON-LINEARITY; NONLOCAL INITIAL CONDITIONS; SEMILINEAR;

EID: 68349100153     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2009.04.058     Document Type: Article
Times cited : (54)

References (33)
  • 1
    • 0028878140 scopus 로고
    • A fractional calculus approach of self-similar protein dynamics
    • Glockle W.G., and Nonnemacher T.F. A fractional calculus approach of self-similar protein dynamics. Biophys. J. 68 (1995) 46-53
    • (1995) Biophys. J. , vol.68 , pp. 46-53
    • Glockle, W.G.1    Nonnemacher, T.F.2
  • 2
    • 0001044887 scopus 로고
    • Relaxation in filled polymers: A fractional calculus approach
    • Metzler F., Schick W., Kilian H.G., and Nonnemacher T.F. Relaxation in filled polymers: A fractional calculus approach. J. Chem. Phys. 103 (1995) 7180-7186
    • (1995) J. Chem. Phys. , vol.103 , pp. 7180-7186
    • Metzler, F.1    Schick, W.2    Kilian, H.G.3    Nonnemacher, T.F.4
  • 7
    • 64249112537 scopus 로고    scopus 로고
    • Existence results for nonlinear boundary value problems of fractional integrodifferential equations with integral boundary conditions
    • 11 pages. Article ID 708576
    • Ahmad B., and Nieto J.J. Existence results for nonlinear boundary value problems of fractional integrodifferential equations with integral boundary conditions. Boundary Value Problems 2009 (2009) 11 pages. Article ID 708576
    • (2009) Boundary Value Problems , vol.2009
    • Ahmad, B.1    Nieto, J.J.2
  • 8
    • 77949264980 scopus 로고    scopus 로고
    • R.P. Agarwal, M. Benchohar, S. Hamani, A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions, Acta Appl. Math. (2008), doi:10.1007/s10440-008-9356-6
    • R.P. Agarwal, M. Benchohar, S. Hamani, A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions, Acta Appl. Math. (2008), doi:10.1007/s10440-008-9356-6
  • 9
    • 25144460994 scopus 로고    scopus 로고
    • Positive solutions for boundary value problem of nonlinear fractional differential equations
    • Bai Z., and Lü H. Positive solutions for boundary value problem of nonlinear fractional differential equations. J. Math. Anal. Appl. 311 (2005) 495-505
    • (2005) J. Math. Anal. Appl. , vol.311 , pp. 495-505
    • Bai, Z.1    Lü, H.2
  • 11
    • 34848916710 scopus 로고    scopus 로고
    • Existence results for fractional order functional differential equations with infinite delay
    • Benchohra M., Henderson J., Ntouyas S.K., and Ouahab A. Existence results for fractional order functional differential equations with infinite delay. J. Math. Anal. Appl. 338 (2008) 1340-1350
    • (2008) J. Math. Anal. Appl. , vol.338 , pp. 1340-1350
    • Benchohra, M.1    Henderson, J.2    Ntouyas, S.K.3    Ouahab, A.4
  • 12
    • 58149196822 scopus 로고    scopus 로고
    • Existence results for fractional functional differential inclusions with infinite delay and application to control theory
    • Benchohra M., Henderson J., Ntouyas S.K., and Ouahab A. Existence results for fractional functional differential inclusions with infinite delay and application to control theory. Fract. Calc. Appl. Anal. 11 (2008) 35-56
    • (2008) Fract. Calc. Appl. Anal. , vol.11 , pp. 35-56
    • Benchohra, M.1    Henderson, J.2    Ntouyas, S.K.3    Ouahab, A.4
  • 13
    • 58049138945 scopus 로고    scopus 로고
    • Some new existence results for fractional differential inclusions with boundary conditions
    • Chang Y.K., and Nieto J.J. Some new existence results for fractional differential inclusions with boundary conditions. Math. Comput. Modelling 49 (2009) 605-609
    • (2009) Math. Comput. Modelling , vol.49 , pp. 605-609
    • Chang, Y.K.1    Nieto, J.J.2
  • 14
    • 0030528474 scopus 로고    scopus 로고
    • Existence and uniqueness for a nonlinear fractional differential equation
    • Delbosco D., and Rodino L. Existence and uniqueness for a nonlinear fractional differential equation. J. Math. Anal. Appl. 204 (1996) 609-625
    • (1996) J. Math. Anal. Appl. , vol.204 , pp. 609-625
    • Delbosco, D.1    Rodino, L.2
  • 15
    • 0032115069 scopus 로고    scopus 로고
    • Nonlinear functional differential equations of arbitrary orders
    • El-Sayed A.M.A. Nonlinear functional differential equations of arbitrary orders. Nonlinear Anal. 33 (1998) 181-186
    • (1998) Nonlinear Anal. , vol.33 , pp. 181-186
    • El-Sayed, A.M.A.1
  • 16
    • 58149197948 scopus 로고    scopus 로고
    • Fractional functional differential inclusions with finite delay
    • Henderson J., and Ouahab A. Fractional functional differential inclusions with finite delay. Nonlinear Anal. 70 (2009) 2091-2105
    • (2009) Nonlinear Anal. , vol.70 , pp. 2091-2105
    • Henderson, J.1    Ouahab, A.2
  • 17
    • 50349092768 scopus 로고    scopus 로고
    • Existence of the mild solution for fractional semilinear initial value problems
    • Jaradat O.K., Al-Omari A., and Momani S. Existence of the mild solution for fractional semilinear initial value problems. Nonlinear Anal. 69 (2008) 3153-3159
    • (2008) Nonlinear Anal. , vol.69 , pp. 3153-3159
    • Jaradat, O.K.1    Al-Omari, A.2    Momani, S.3
  • 18
    • 51349163878 scopus 로고    scopus 로고
    • Theory of fractional differential equations in a Banach space
    • Lakshmikantham V., and Devi J.V. Theory of fractional differential equations in a Banach space. Eur. J. Pure Appl. Math. 1 (2008) 38-45
    • (2008) Eur. J. Pure Appl. Math. , vol.1 , pp. 38-45
    • Lakshmikantham, V.1    Devi, J.V.2
  • 22
    • 58149231350 scopus 로고    scopus 로고
    • A Cauchy problem for some fractional abstract differential equation with nonlocal conditions
    • N'Guérékata G.M. A Cauchy problem for some fractional abstract differential equation with nonlocal conditions. Nonlinear Anal. 70 (2009) 1873-1876
    • (2009) Nonlinear Anal. , vol.70 , pp. 1873-1876
    • N'Guérékata, G.M.1
  • 24
    • 84948514180 scopus 로고
    • Theorems about existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space
    • Byszewski L., and Lakshmikantham V. Theorems about existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space. Appl. Anal. 40 (1990) 11-19
    • (1990) Appl. Anal. , vol.40 , pp. 11-19
    • Byszewski, L.1    Lakshmikantham, V.2
  • 25
    • 44949272606 scopus 로고
    • Theorems about the existence and uniqueness of a solution of a semilinear evolution nonlocal Cauchy problem
    • Byszewski L. Theorems about the existence and uniqueness of a solution of a semilinear evolution nonlocal Cauchy problem. J. Math. Anal. Appl. 162 (1991) 496-505
    • (1991) J. Math. Anal. Appl. , vol.162 , pp. 496-505
    • Byszewski, L.1
  • 27
    • 0000297319 scopus 로고
    • Exponential decay of solutions of semilinear parabolic equations with nonlocal initial conditions
    • Deng K. Exponential decay of solutions of semilinear parabolic equations with nonlocal initial conditions. J. Math. Anal. Appl. 179 (1993) 630-637
    • (1993) J. Math. Anal. Appl. , vol.179 , pp. 630-637
    • Deng, K.1
  • 28
    • 0038137295 scopus 로고    scopus 로고
    • Existence of solutions for neutral functional differential evolution equations with nonlocal conditions
    • Fu X., and Ezzinbi K. Existence of solutions for neutral functional differential evolution equations with nonlocal conditions. Nonlinear Anal. 54 (2003) 215-227
    • (2003) Nonlinear Anal. , vol.54 , pp. 215-227
    • Fu, X.1    Ezzinbi, K.2
  • 29
    • 61549131656 scopus 로고    scopus 로고
    • Existence for a class of partial differential equations with nonlocal conditions
    • Liu H., and Chang J.C. Existence for a class of partial differential equations with nonlocal conditions. Nonlinear Anal. 70 (2009) 3076-3083
    • (2009) Nonlinear Anal. , vol.70 , pp. 3076-3083
    • Liu, H.1    Chang, J.C.2
  • 30
    • 46249090894 scopus 로고    scopus 로고
    • Existence results on semi-infinite intervals for nonlinear evolution equations and inclusions via semigroup theory
    • Ntouyas S.K., and O'Regan D. Existence results on semi-infinite intervals for nonlinear evolution equations and inclusions via semigroup theory. Numer. Funct. Anal. Optim. 29 (2008) 419-444
    • (2008) Numer. Funct. Anal. Optim. , vol.29 , pp. 419-444
    • Ntouyas, S.K.1    O'Regan, D.2
  • 31
    • 33947310146 scopus 로고    scopus 로고
    • Existence of solutions for impulsive partial neutral functional differential equations
    • Hernández E., Rabello M., and Henríquez H. Existence of solutions for impulsive partial neutral functional differential equations. J. Math. Anal. Appl. 331 (2007) 1135-1158
    • (2007) J. Math. Anal. Appl. , vol.331 , pp. 1135-1158
    • Hernández, E.1    Rabello, M.2    Henríquez, H.3
  • 32
    • 29344431971 scopus 로고
    • Springer-Verlag, New York
    • Pazy A. Semigroups of Linear Operators and Applications to Partial Equations. Applied Mathematical Sciences vol. 44 (1983), Springer-Verlag, New York
    • (1983) Applied Mathematical Sciences , vol.44
    • Pazy, A.1
  • 33
    • 0001954809 scopus 로고
    • On a fixed point principle
    • Sadovskii B.N. On a fixed point principle. Funct. Anal. Appl. 1 (1967) 74-76
    • (1967) Funct. Anal. Appl. , vol.1 , pp. 74-76
    • Sadovskii, B.N.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.