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Volumn 12, Issue 1, 2011, Pages 3-16

Existence theory for impulsive partial hyperbolic differential equations of fractional order at variable times

Author keywords

Caputo fractional order derivative; Fixed point; Fractional order; Impulsive hyperbolic differential equations; Left sided mixed Riemann Liouville integral; Solution; Variable times

Indexed keywords


EID: 79952549672     PISSN: 15835022     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (3)

References (51)
  • 1
    • 77249153545 scopus 로고    scopus 로고
    • Partial hyperbolic differential equations with finite delay involving the Caputo fractional derivative
    • S. Abbas, M. Benchohra, Partial hyperbolic differential equations with finite delay involving the Caputo fractional derivative, Commun. Math. Anal., 7(2009), 62-72.
    • (2009) Commun. Math. Anal. , vol.7 , pp. 62-72
    • Abbas, S.1    Benchohra, M.2
  • 2
    • 68949186567 scopus 로고    scopus 로고
    • Darboux problem for perturbed partial differential equations of fractional order with finite delay
    • S. Abbas, M. Benchohra, Darboux problem for perturbed partial differential equations of fractional order with finite delay, Nonlinear Anal. Hybrid Syst., 3(2009), 597-604.
    • (2009) Nonlinear Anal. Hybrid Syst. , vol.3 , pp. 597-604
    • Abbas, S.1    Benchohra, M.2
  • 3
    • 77949264980 scopus 로고    scopus 로고
    • A survey on existence result for boundary value problems of nonlinear fractional differential equations and inclusions
    • R.P. Agarwal, M. Benchohra, S. Hamani, A survey on existence result for boundary value problems of nonlinear fractional differential equations and inclusions, Acta. Appl. Math., 109(2010), no. 3, 973-1033.
    • (2010) Acta. Appl. Math. , vol.109 , Issue.3 , pp. 973-1033
    • Agarwal, R.P.1    Benchohra, M.2    Hamani, S.3
  • 5
    • 76649109382 scopus 로고    scopus 로고
    • Impulsive fractional differential inclusions involving the Caputo fractional derivative
    • E. Ait Dads, M. Benchohra, S. Hamani, Impulsive fractional differential inclusions involving the Caputo fractional derivative, Fract. Calc. Appl. Anal., 12(2009), no. 1, 15-38.
    • (2009) Fract. Calc. Appl. Anal. , vol.12 , Issue.1 , pp. 15-38
    • Ait Dads, E.1    Benchohra, M.2    Hamani, S.3
  • 6
    • 0030588772 scopus 로고    scopus 로고
    • Periodic boundary value problem for first order differential equations with impulses at variable times
    • DOI 10.1006/jmaa.1996.0424
    • I. Bajo, E. Liz, Periodic boundary value problem for first order differential equations with impulses at variable times, J. Math. Anal. Appl., 204(1996), 65-73. (Pubitemid 126171221)
    • (1996) Journal of Mathematical Analysis and Applications , vol.204 , Issue.1 , pp. 65-73
    • Bajo, I.1    Liz, E.2
  • 8
    • 33750985067 scopus 로고    scopus 로고
    • Existence theory for perturbed impulsive hyperbolic differential inclusions with variable times
    • DOI 10.1016/j.jmaa.2006.05.003, PII S0022247X06004781
    • A. Belarbi, M. Benchohra, Existence theory for perturbed impulsive hyperbolic differential inclusions with variable times, J. Math. Anal. Appl., 327(2007), 1116-1129. (Pubitemid 44742797)
    • (2007) Journal of Mathematical Analysis and Applications , vol.327 , Issue.2 , pp. 1116-1129
    • Belarbi, A.1    Benchohra, M.2
  • 9
    • 38149134242 scopus 로고    scopus 로고
    • Uniqueness results for fractional functional differential equations with infinite delay in Frechet spaces
    • A. Belarbi, M. Benchohra, A. Ouahab, Uniqueness results for fractional functional differential equations with infinite delay in Frechet spaces, Appl. Anal., 85(2006), 1459-1470.
    • (2006) Appl. Anal. , vol.85 , pp. 1459-1470
    • Belarbi, A.1    Benchohra, M.2    Ouahab, A.3
  • 11
    • 33751007351 scopus 로고    scopus 로고
    • Existence Results for Impulsive Hyperbolic Differential Inclusions
    • DOI 10.1080/00036810310001613160
    • M. Benchohra, L. Góorniewicz, S.K. Ntouyas, A. Ouahab, Existence results for impulsive hyperbolic differential inclusions, Appl. Anal., 82(2003), 1085-1097. (Pubitemid 37422087)
    • (2003) APPLICABLE ANALYSIS , vol.82 , Issue.11 , pp. 1085-1097
    • Benchohra, M.1    Gorniewicz, L.2    Ntouyas, S.K.3    Ouahab, A.4
  • 12
    • 58249117112 scopus 로고    scopus 로고
    • Existence results for boundary value problems with nonlinear fractional differential equations
    • M. Benchohra, J.R. Graef, S. Hamani, Existence results for boundary value problems with nonlinear fractional differential equations, Appl. Anal., 87(2008), no. 7, 851-863.
    • (2008) Appl. Anal. , vol.87 , Issue.7 , pp. 851-863
    • Benchohra, M.1    Graef, J.R.2    Hamani, S.3
  • 13
    • 58249103422 scopus 로고    scopus 로고
    • Boundary value problems for differential equations with fractional order
    • M. Benchohra, S. Hamani, S.K. Ntouyas, Boundary value problems for differential equations with fractional order, Surv. Math. Appl., 3(2008), 1-12.
    • (2008) Surv. Math. Appl. , vol.3 , pp. 1-12
    • Benchohra, M.1    Hamani, S.2    Ntouyas, S.K.3
  • 15
    • 34848916710 scopus 로고    scopus 로고
    • Existence results for functional differential equations of fractional order
    • M. Benchohra, J. Henderson, S.K. Ntouyas, A. Ouahab, Existence results for functional differential equations of fractional order, 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
  • 16
    • 3042579835 scopus 로고    scopus 로고
    • Impulsive neutral functional differential inclusions with variable times
    • M. Benchohra, J.A. Ouahab, Impulsive neutral functional differential inclusions with variable times, Electron. J. Differential Equations, 2003(2003), no. 67, 1-12. (Pubitemid 38817774)
    • (2003) Electronic Journal of Differential Equations , vol.2003 , pp. 1-12
    • Benchohra, M.1    Ouahab, A.2
  • 17
    • 58249118048 scopus 로고    scopus 로고
    • Existence and uniqueness of solutions to impulsive fractional differential equations
    • M. Benchohra, B.A. Slimani, Existence and uniqueness of solutions to impulsive fractional differential equations, Electron. J. Differential Equations, 2009(2009), no. 10, 11 pp.
    • (2009) Electron. J. Differential Equations , vol.2009 , Issue.10 , pp. 11
    • Benchohra, M.1    Slimani, B.A.2
  • 18
    • 84959979133 scopus 로고
    • Theorem about existence and uniqueness of continuous solutions of nonlocal problem for nonlinear hyperbolic equation
    • L. Byszewski, Theorem about existence and uniqueness of continuous solutions of nonlocal problem for nonlinear hyperbolic equation, Appl. Anal., 40(1991), 173-180.
    • (1991) Appl. Anal. , vol.40 , pp. 173-180
    • Byszewski, L.1
  • 19
    • 33644541223 scopus 로고
    • Differential and functional-differential problems with nonlocal conditions, (in Polish)
    • Krakow
    • L. Byszewski, Differential and functional-differential problems with nonlocal conditions, (in Polish), Cracow University of Technology Monograph, 184, Krakow, 1995.
    • (1995) Cracow University of Technology Monograph , vol.184
    • Byszewski, L.1
  • 22
    • 0037081673 scopus 로고    scopus 로고
    • Analysis of fractional differential equations
    • K. Diethelm, N.J. Ford, Analysis of fractional differential equations, J. Math. Anal. Appl., 265 (2002), 229-248.
    • (2002) J. Math. Anal. Appl. , vol.265 , pp. 229-248
    • Diethelm, K.1    Ford, N.J.2
  • 24
    • 0142103339 scopus 로고    scopus 로고
    • First order impulsive initial and periodic problems with variable moments
    • M. Frigon, D. O'Regan, First order impulsive initial and periodic problems with variable moments, J. Math. Anal. Appl., 233(1999), 730-739.
    • (1999) J. Math. Anal. Appl. , vol.233 , pp. 730-739
    • Frigon, M.1    O'Regan, D.2
  • 25
    • 0142071710 scopus 로고    scopus 로고
    • Second order Sturm-Liouville BVP's with impulses at variable moments
    • M. Frigon, D. O'Regan, Second order Sturm-Liouville BVP's with impulses at variable moments, Dynam. Contin. Discrete Impuls. Systems, 8 (2001), no. 2, 149-159.
    • (2001) Dynam. Contin. Discrete Impuls. Systems , vol.8 , Issue.2 , pp. 149-159
    • Frigon, M.1    O'Regan, D.2
  • 26
    • 0028878140 scopus 로고
    • A fractional calculus approach of selfsimilar protein dynamics
    • W.G. Glockle, T.F. Nonnenmacher, A fractional calculus approach of selfsimilar protein dynamics, Biophys. J., 68(1995), 46-53.
    • (1995) Biophys. J. , vol.68 , pp. 46-53
    • Glockle, W.G.1    Nonnenmacher, T.F.2
  • 29
    • 0028423627 scopus 로고
    • Extremal solutions, comparison principle and stability criteria for impulsive differential equations with variable times
    • S.K. Kaul, V. Lakshmikantham, S. Leela, Extremal solutions, comparison principle and stability criteria for impulsive differential equations with variable times, Nonlinear Anal., 22(1994), 1263-1270.
    • (1994) Nonlinear Anal. , vol.22 , pp. 1263-1270
    • Kaul, S.K.1    Lakshmikantham, V.2    Leela, S.3
  • 31
    • 27844552286 scopus 로고    scopus 로고
    • Differential difference inequalities related to hyperbolic functional differential systems and applications
    • Z. Kamont, K. Kropielnicka, Differential difference inequalities related to hyperbolic functional differential systems and applications, Math. Inequal. Appl., 8(2005), no. 4, 655-674. (Pubitemid 41639388)
    • (2005) Mathematical Inequalities and Applications , vol.8 , Issue.4 , pp. 655-674
    • Kamont, Z.1    Kropielnicka, K.2
  • 32
    • 0142103340 scopus 로고    scopus 로고
    • Vector Lyapunov functions for impulsive differential systems with variable times
    • S.K. Kaul, X.Z. Liu, Vector Lyapunov functions for impulsive differential systems with variable times, Dynam. Contin. Discrete Impuls. Systems, 6(1999), 25-38.
    • (1999) Dynam. Contin. Discrete Impuls. Systems , vol.6 , pp. 25-38
    • Kaul, S.K.1    Liu, X.Z.2
  • 33
    • 0142039838 scopus 로고    scopus 로고
    • Impulsive integro-differential equations with variable times
    • S.K. Kaul, X.Z. Liu, Impulsive integro-differential equations with variable times, Nonlinear Stud., 8(2001), 21-32.
    • (2001) Nonlinear Stud. , vol.8 , pp. 21-32
    • Kaul, S.K.1    Liu, X.Z.2
  • 34
    • 71849110089 scopus 로고    scopus 로고
    • Nonlinear differential equations of fractional order in a space of integrable functions
    • A.A. Kilbas, B. Bonilla, J. Trujillo, Nonlinear differential equations of fractional order in a space of integrable functions, Dokl. Ross. Akad. Nauk, 374(2000), no. 4, 445-449.
    • (2000) Dokl. Ross. Akad. Nauk , vol.374 , Issue.4 , pp. 445-449
    • Kilbas, A.A.1    Bonilla, B.2    Trujillo, J.3
  • 35
    • 17444382726 scopus 로고    scopus 로고
    • Nonlinear differential equations with the Caputo fractional derivative in the space of continuously differentiable functions
    • DOI 10.1007/s10625-005-0137-y
    • A.A. Kilbas, S.A. Marzan, Nonlinear differential equations with the Caputo fractional derivative in the space of continuously differentiable functions, Differential Equations, 41(2005), 84-89. (Pubitemid 40551100)
    • (2005) Differential Equations , vol.41 , Issue.1 , pp. 84-89
    • Kilbas, A.A.1    Marzan, S.A.2
  • 39
    • 0142071711 scopus 로고
    • The method of upper and lower solutions and monotone technique for impulsive differential equations with variable moments
    • V. Lakshmikantham, N.S. Papageorgiou, J. Vasundhara, The method of upper and lower solutions and monotone technique for impulsive differential equations with variable moments, Appl. Anal., 15 (1993), 41-58.
    • (1993) Appl. Anal. , vol.15 , pp. 41-58
    • Lakshmikantham, V.1    Papageorgiou, N.S.2    Vasundhara, J.3
  • 40
    • 0022020055 scopus 로고
    • METHOD OF UPPER, LOWER SOLUTIONS AND HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS.
    • DOI 10.1016/0022-247X(85)90062-9
    • V. Lakshmikantham, S.G. Pandit, The method of upper, lower solutions and hyperbolic partial differential equations, J. Math. Anal. Appl., 105(1985), 466-477. (Pubitemid 15598644)
    • (1985) Journal of Mathematical Analysis and Applications , vol.105 , Issue.2 , pp. 466-477
    • Lakshmikantham, V.1    Pandit, S.G.2
  • 41
    • 0001983732 scopus 로고    scopus 로고
    • Fractional calculus: Some basic problems in continuum and statistical mechanics
    • (A. Carpinteri and F. Mainardi, Eds.), Springer-Verlag, Wien
    • F. Mainardi, Fractional calculus: Some basic problems in continuum and statistical mechanics, in "Fractals and Fractional Calculus in Continuum Mechanics" (A. Carpinteri and F. Mainardi, Eds.), Springer-Verlag, Wien, 1997, 291-348.
    • (1997) Fractals and Fractional Calculus in Continuum Mechanics , pp. 291-348
    • Mainardi, F.1
  • 42
    • 0001044887 scopus 로고
    • Relaxation in filled polymers: A fractional calculus approach
    • F. Metzler, W. Schick, H.G. Kilian, T.F. Nonnenmacher, 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    Nonnenmacher, T.F.4
  • 43
    • 71549128004 scopus 로고    scopus 로고
    • Existence and uniqueness of mild solutions to impulsive fractional differential equations
    • G. Mophou, Existence and uniqueness of mild solutions to impulsive fractional differential equations, Nonlinear Anal., 72(2010), 1604-1615.
    • (2010) Nonlinear Anal. , vol.72 , pp. 1604-1615
    • Mophou, G.1
  • 44
    • 0043047275 scopus 로고    scopus 로고
    • Monotone methods for systems of nonlinear hyperbolic problems in two independent variables
    • S.G. Pandit, Monotone methods for systems of nonlinear hyperbolic problems in two independent variables, Nonlinear Anal., 30(1997), 235-272.
    • (1997) Nonlinear Anal. , vol.30 , pp. 235-272
    • Pandit, S.G.1
  • 48
    • 0040644408 scopus 로고
    • On one class of differential equations of noninteger order
    • N.P. Semenchuk, On one class of differential equations of noninteger order, Differents. Uravn., 10 (1982), 1831-1833.
    • (1982) Differents. Uravn. , vol.10 , pp. 1831-1833
    • Semenchuk, N.P.1
  • 49
    • 68949195303 scopus 로고    scopus 로고
    • Existence of solutions of partial differential inclusions of fractional order
    • A.N. Vityuk, Existence of solutions of partial differential inclusions of fractional order, Izv. Vyssh. Uchebn., Ser. Mat., 8(1997), 13-19.
    • (1997) Izv. Vyssh. Uchebn., Ser. Mat. , vol.8 , pp. 13-19
    • Vityuk, A.N.1
  • 50
    • 68949171371 scopus 로고    scopus 로고
    • Existence of solutions of systems of partial differential equations of fractional order
    • A.N. Vityuk, A.V. Golushkov, Existence of solutions of systems of partial differential equations of fractional order, Nonlinear Oscil., 7(2004), no. 3, 318-325.
    • (2004) Nonlinear Oscil. , vol.7 , Issue.3 , pp. 318-325
    • Vityuk, A.N.1    Golushkov, A.V.2
  • 51
    • 33645152919 scopus 로고    scopus 로고
    • Positive solutions for boundary-value problems of nonlinear fractional diffrential equations
    • S. Zhang, Positive solutions for boundary-value problems of nonlinear fractional diffrential equations, Electron. J. Differential Equations, 2006(2006), no. 36, 12 pp.
    • (2006) Electron. J. Differential Equations , vol.2006 , Issue.36 , pp. 12
    • Zhang, S.1


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