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Volumn 43, Issue 4, 2010, Pages 775-797

Impulsive partial hyperbolic differential inclusions of fractional order

Author keywords

Caputo fractional order derivative; Fixed point; Fractional order; Impulsive differential inclusions; Left sided mixed Riemann Liouville integral; Solution

Indexed keywords


EID: 84945330794     PISSN: 04201213     EISSN: 23914661     Source Type: Journal    
DOI: 10.1515/dema-2010-0406     Document Type: Article
Times cited : (3)

References (53)
  • 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. 3 (2009), 597-604.
    • (2009) Nonlinear Anal. , 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 (3) (2010), 973-1033; DOI 10.1007/sl0440-008-9356-6.
    • (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, Pract. Calc. Appl. Anal. 12 (1) (2009), 15-38.
    • (2009) Pract. Calc. Appl. Anal. , vol.12 , Issue.1 , pp. 15-38
    • Ait Dads, E.1    Benchohra, M.2    Hamani, S.3
  • 7
    • 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
  • 8
    • 58249117112 scopus 로고    scopus 로고
    • Existence results for boundary value problems of nonlinear fractional differential equations with integral conditions
    • M. Benchohra, J. R. Graef, S. Hamani, Existence results for boundary value problems of nonlinear fractional differential equations with integral conditions, Appl. Anal. 87 (7) (2008), 851-863.
    • (2008) Appl. Anal. , vol.87 , Issue.7 , pp. 851-863
    • Benchohra, M.1    Graef, J.R.2    Hamani, S.3
  • 9
    • 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
  • 11
    • 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
  • 12
    • 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 10 (2009), 1-11.
    • (2009) Electron. J. Differential Equations , vol.10 , pp. 1-11
    • Benchohra, M.1    Slimani, B.A.2
  • 14
    • 0002110530 scopus 로고
    • Extensions and selections of maps with decomposable values
    • A. Bressan, G. Colombo, Extensions and selections of maps with decomposable values, Studia Math. 90 (1988), 69-86.
    • (1988) Studia Math. , vol.90 , pp. 69-86
    • Bressan, A.1    Colombo, G.2
  • 16
    • 58049138945 scopus 로고    scopus 로고
    • Some new existence results for fractional differential inclusions with boundary conditions
    • Y.-K. Chang, J. J. Nieto, Some new existence results for fractional differential inclusions with boundary conditions, Math. Comput. Model. 49 (2009), 605-609.
    • (2009) Math. Comput. Model. , vol.49 , pp. 605-609
    • Chang, Y.-K.1    Nieto, J.J.2
  • 17
    • 51249191814 scopus 로고
    • Multivalued contraction mappings in generalized metric spaces
    • H. Covitz, S. B. Nadler Jr., Multivalued contraction mappings in generalized metric spaces, Israel J. Math. 8 (1970), 5-11.
    • (1970) Israel J. Math. , vol.8 , pp. 5-11
    • Covitz, H.1    Nadler, S.B.2
  • 20
  • 21
    • 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
  • 22
    • 0002687438 scopus 로고
    • Theeoremes d'existence de solutions d'inclusions diffeerentielles, Topological Methods in Differential Equations and Inclusions
    • edited by A. Granas and M. Frigon, Kluwer Academic Publishers, Dordrecht
    • M. Frigon, Theeoremes d'existence de solutions d'inclusions diffeerentielles, Topological Methods in Differential Equations and Inclusions (edited by A. Granas and M. Frigon), NATO ASI Series C, Vol. 472, Kluwer Academic Publishers, Dordrecht, 1995, 51-87.
    • (1995) NATO ASI Series C , vol.472 , pp. 51-87
    • Frigon, M.1
  • 25
    • 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
  • 27
    • 0006899383 scopus 로고    scopus 로고
    • Topological fixed point theory of multivalued mappings
    • Kluwer Academic Publishers, Dordrecht
    • L. Gorniewicz, Topological Fixed Point Theory of Multivalued Mappings, Mathematics and its Applications, 495, Kluwer Academic Publishers, Dordrecht, 1999.
    • (1999) Mathematics and Its Applications , vol.495
    • Gorniewicz, L.1
  • 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 (4) (2005), 655-674.
    • (2005) Math. Inequal. Appl. , vol.8 , Issue.4 , pp. 655-674
    • Kamont, Z.1    Kropielnicka, K.2
  • 32
    • 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 (4) (2000), 445-449.
    • (2000) Dokl. Ross. Akad. Nauk , vol.374 , Issue.4 , pp. 445-449
    • Kilbas, A.A.1    Bonilla, B.2    Trujillo, J.3
  • 33
    • 17444382726 scopus 로고    scopus 로고
    • Nonlinear differential equations with the Caputo fractional derivative in the space of continuously differentiable functions
    • 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.
    • (2005) Differential Equations , vol.41 , pp. 84-89
    • Kilbas, A.A.1    Marzan, S.A.2
  • 38
    • 0000017706 scopus 로고
    • An application of the Kakutani-Ky Fan theorem in the theory of ordinary differential equations
    • A. Lasota, Z. Opial, An application of the Kakutani-Ky Fan theorem in the theory of ordinary differential equations, Bull. Acad. Pol. Sci. Ser. Sci. Math. Astronom. Phys. 13 (1965), 781-786.
    • (1965) Bull. Acad. Pol. Sci. Ser. Sci. Math. Astronom. Phys. , vol.13 , pp. 781-786
    • Lasota, A.1    Opial, Z.2
  • 39
    • 0022020055 scopus 로고
    • The Method of upper, lower solutions and hyperbolic partial differential equations
    • V. Lakshmikantham, S. G. Pandit, The Method of upper, lower solutions and hyperbolic partial differential equations, J. Math. Anal. Appl. 105 (1985), 466-477.
    • (1985) J. Math. Anal. Appl. , vol.105 , pp. 466-477
    • Lakshmikantham, V.1    Pandit, S.G.2
  • 40
    • 0001983732 scopus 로고    scopus 로고
    • Fractional calculus: Some basic problems in continuum and statistical mechanics
    • A. Carpin-teri 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. Carpin-teri and F. Mainardi (eds), pp. 291-348, Springer-Verlag, Wien, 1997.
    • (1997) Fractals and Fractional Calculus in Continuum Mechanics , pp. 291-348
    • Mainardi, F.1
  • 41
    • 0002547746 scopus 로고
    • A Rothe's type theorem for non-compact acyclic-valued map
    • M. Martelli, A Rothe's type theorem for non-compact acyclic-valued map, Boll. Un. Mat. Ital. 4 (3), (1975), 70-76.
    • (1975) Boll. Un. Mat. Ital. , vol.4 , Issue.3 , pp. 70-76
    • Martelli, M.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
    • 34147123779 scopus 로고    scopus 로고
    • Existence and uniqueness results for impulsive functional differential equations with scalar multiple delay and infinite delay
    • A. Ouahab, Existence and uniqueness results for impulsive functional differential equations with scalar multiple delay and infinite delay, Nonlinear Anal. 67 (2007), 1027-1041.
    • (2007) Nonlinear Anal. , vol.67 , pp. 1027-1041
    • Ouahab, A.1
  • 45
    • 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
  • 49
    • 0040644408 scopus 로고
    • On one class of differential equations of noninteger order
    • N. P. Semenchuk, On one class of differential equations of noninteger order, Differ-ents. Uravn. 10 (1982), 1831-1833.
    • (1982) Differ-Ents. Uravn. , vol.10 , pp. 1831-1833
    • Semenchuk, N.P.1
  • 51
    • 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
  • 52
    • 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 (3) (2004), 318-325.
    • (2004) Nonlinear Oscil. , vol.7 , Issue.3 , pp. 318-325
    • Vityuk, A.N.1    Golushkov, A.V.2
  • 53
    • 33645152919 scopus 로고    scopus 로고
    • Positive solutions for boundary-value problems of nonlinear fractional dif- frential equations
    • S. Zhang, Positive solutions for boundary-value problems of nonlinear fractional dif- frential equations, Electron. J. Differential Equations 36 (2006), 1-12.
    • (2006) Electron. J. Differential Equations , vol.36 , pp. 1-12
    • Zhang, S.1


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