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Volumn 2011, Issue , 2011, Pages

Existence of solutions to fractional order ordinary and delay differential equations and applications

Author keywords

Fixed point theorems; Fractional differential equation; Maximum interval of existence

Indexed keywords


EID: 79952143093     PISSN: None     EISSN: 10726691     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (102)

References (43)
  • 1
    • 78049476732 scopus 로고    scopus 로고
    • Pseudo almost automorphic solutions of fractional order neutral differential equation
    • Abbas, S.; Pseudo almost automorphic solutions of fractional order neutral differential equation, Semigroup Forum, Volume 81, Number 3 (2010), 393-404.
    • (2010) Semigroup Forum , vol.81 , Issue.3 , pp. 393-404
    • Abbas, S.1
  • 2
    • 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 Math. J., 16, 3 (2009), 401-411.
    • (2009) Georgian Math. J. , vol.16 , Issue.3 , pp. 401-411
    • Agarwal, R.P.1    Benchohra, M.2    Hamani, S.3
  • 3
    • 74149092568 scopus 로고    scopus 로고
    • Existence of fractional neutral functional differential equations
    • Agarwal, R.P.; Zhou, Y.; He, Y.; Existence of fractional neutral functional differential equations Comp. Math. Appl., 59, 3 (2010), 1095-1100.
    • (2010) Comp. Math. Appl. , vol.59 , Issue.3 , pp. 1095-1100
    • Agarwal, R.P.1    Zhou, Y.2    He, Y.3
  • 4
    • 33750295344 scopus 로고    scopus 로고
    • Equilibrium points, stability and numerical solutions of fractional-order predator-prey and rabies models
    • Ahmed, E.; El-Sayed, A. M. A.; El-Saka, H. A. A.; Equilibrium points, stability and numerical solutions of fractional-order predator-prey and rabies models. J. Math. Anal. Appl., Vol. 325 (2007), no. 1, 542-553.
    • (2007) J. Math. Anal. Appl. , vol.325 , Issue.1 , pp. 542-553
    • Ahmed, E.1    El-Sayed, A.M.A.2    El-Saka, H.A.A.3
  • 5
    • 78149410275 scopus 로고    scopus 로고
    • A new approach to the theory of functional integral equations of fractional order
    • Banas, J.; Zajac, T.; A new approach to the theory of functional integral equations of fractional order J. Math. Anal. Appl., 375, 2 (2011), 375-387.
    • (2011) J. Math. Anal. Appl. , vol.375 , Issue.2 , pp. 375-387
    • Banas, J.1    Zajac, T.2
  • 6
    • 2442548776 scopus 로고    scopus 로고
    • Analysis of a system of fractional differential equations
    • Daftardar-Gdjji, Varsha; Babakhani, A.; Analysis of a system of fractional differential equations, J. Math. Anal. Appl. 293 (2004), 511-522.
    • (2004) J. Math. Anal. Appl. , vol.293 , pp. 511-522
    • Daftardar-Gdjji, V.1    Babakhani, A.2
  • 8
    • 0030528474 scopus 로고    scopus 로고
    • Existence and uniqueness for a nonlinear fractional differential equation
    • Delbosco, D.; 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
  • 9
    • 77950188013 scopus 로고    scopus 로고
    • Existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations
    • Deng, J.; Ma, L.; Existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations, Appl. Math. Lett., 23, 6 (2010), 676-680.
    • (2010) Appl. Math. Lett. , vol.23 , Issue.6 , pp. 676-680
    • Deng, J.1    Ma, L.2
  • 10
    • 0037081673 scopus 로고    scopus 로고
    • Analysis of fractional differential equations
    • Diethelm, K.; Neville 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    Neville Ford, J.2
  • 11
    • 79953727346 scopus 로고    scopus 로고
    • The analysis of fractional differential equations
    • Diethelm, K.; The analysis of fractional differential equations, Springer, 2010.
    • (2010) Springer
    • Diethelm, K.1
  • 12
    • 0011642556 scopus 로고
    • Fractional order differential equation
    • El-Sayed,A. M. A.; Fractional order differential equation, Kyungpook Math. J., Vol. 28, 2 (1988), 18-22.
    • (1988) Kyungpook Math. J. , vol.28 , Issue.2 , pp. 18-22
    • El-Sayed, A.M.A.1
  • 13
    • 44049116967 scopus 로고
    • On the fractional differential equations
    • El-Sayed, A. M. A.; On the fractional differential equations. Appl. Math. Comput., Vol. 49 (1992), no. 2-3, 205-213,
    • (1992) Appl. Math. Comput. , vol.49 , Issue.2-3 , pp. 205-213
    • El-Sayed, A.M.A.1
  • 14
    • 0032115069 scopus 로고    scopus 로고
    • Nonlinear functional-differential equations of arbitrary orders
    • El-Sayed, Ahmed M. A.; Nonlinear functional-differential equations of arbitrary orders. Nonlinear Anal. 33 (1998), no. 2, 181-186.
    • (1998) Nonlinear Anal. , vol.33 , Issue.2 , pp. 181-186
    • El-Sayed Ahmed, M.A.1
  • 16
    • 34147158309 scopus 로고    scopus 로고
    • Long time behavior for a nonlinear fractional model
    • Furati, Khaled M.; Tatar, Nasser-eddine; Long time behavior for a nonlinear fractional model, J. Math. Anal. Appl., 332, 1 (2007), 441-454.
    • (2007) J. Math. Anal. Appl. , vol.332 , Issue.1 , pp. 441-454
    • Furati, K.M.1    Tatar, N.-E.2
  • 17
    • 0037457777 scopus 로고    scopus 로고
    • The problem of the initial conditions and their physical meaning in linear differential equations of fractional order
    • Giannantoni, C.; The problem of the initial conditions and their physical meaning in linear differential equations of fractional order, Appl. Math. Comp., 141, 1 (2003), 87-102.
    • (2003) Appl. Math. Comp. , vol.141 , Issue.1 , pp. 87-102
    • Giannantoni, C.1
  • 18
    • 0003427295 scopus 로고    scopus 로고
    • Hilfer, R. (ed.); World Scientific Publishing Co., Inc., River Edge, NJ
    • Hilfer, R. (ed.); Applications of fractional calculus in physics. World Scientific Publishing Co., Inc., River Edge, NJ, 2000.
    • (2000) Applications of fractional calculus in physics
  • 19
    • 33745869026 scopus 로고    scopus 로고
    • Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives
    • Heymans, N.; Podlubny, I.; Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives. Rheol Acta, 45 (2006), 765-771.
    • (2006) Rheol Acta , vol.45 , pp. 765-771
    • Heymans, N.1    Podlubny, I.2
  • 20
    • 8844229377 scopus 로고
    • Local and global existence theorems on differential equations of non-integer order
    • Hadid, S. B.; Local and global existence theorems on differential equations of non-integer order, J. Fract. Calc., 7 (1995), 101-105.
    • (1995) J. Fract. Calc. , vol.7 , pp. 101-105
    • Hadid, S.B.1
  • 21
    • 17844379086 scopus 로고    scopus 로고
    • On the existence of maximal and minimal solutions of differential equations of non-integer order
    • Hadid, S. B.; Masaedeh S. Momani; On the existence of maximal and minimal solutions of differential equations of non-integer order, J. Fract. Calc. 9 (1996), 41-44.
    • (1996) J. Fract. Calc. , vol.9 , pp. 41-44
    • Hadid, S.B.1    Momani, M.S.2
  • 22
    • 34249295169 scopus 로고    scopus 로고
    • On the existence and uniqueness of solutions of a class of fractional differential equations
    • Ibrahim, Rabha W.; Momani, Shaher; On the existence and uniqueness of solutions of a class of fractional differential equations, J. Math. Anal. Appl. 334 (2007), 1-10.
    • (2007) J. Math. Anal. Appl. , vol.334 , pp. 1-10
    • Ibrahim, R.W.1    Momani, S.2
  • 23
    • 0035129986 scopus 로고    scopus 로고
    • The integral analogue of the Leibniz rule for fractional calculus and its applications involving functions of several variables
    • Jaimini, B. B.; Shrivastava, N.; Srivastava, H. M.; The integral analogue of the Leibniz rule for fractional calculus and its applications involving functions of several variables, Comput. Math. Appl., 41, 1-2 (2001), 149-155.
    • (2001) Comput. Math. Appl. , vol.41 , Issue.1-2 , pp. 149-155
    • Jaimini, B.B.1    Shrivastava, N.2    Srivastava, H.M.3
  • 25
    • 53949111458 scopus 로고    scopus 로고
    • Basic theory of fractional differential equations
    • Lakshmikantham, V.; Vatsala, A. S.; Basic theory of fractional differential equations, Nonlinear Analysis: TMA, 69, 8 (2008), 2677-2682.
    • (2008) Nonlinear Analysis: TMA , vol.69 , Issue.8 , pp. 2677-2682
    • Lakshmikantham, V.1    Vatsala, A.S.2
  • 26
    • 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, Vol-II (2007), 395-402.
    • (2007) Communications in Applied Analysis , vol.2 , pp. 395-402
    • Lakshmikantham, V.1    Vatsala, A.S.2
  • 27
    • 51349139941 scopus 로고    scopus 로고
    • Theory of fractional functional differential equations
    • Lakshmikantham, V.; Theory of fractional functional differential equations, Nonlinear Analysis: TMA, 69, 10 (2008), 3337-3343.
    • (2008) Nonlinear Analysis: TMA , vol.69 , Issue.10 , pp. 3337-3343
    • Lakshmikantham, V.1
  • 29
    • 0001983732 scopus 로고    scopus 로고
    • Fractional Calculus: Some basic problems in continuum and statistical mechanics
    • in, Carpinteri, A. and Mainardi, F. (eds), Springer, New York
    • Mainardi, F.; Fractional Calculus: Some basic problems in continuum and statistical mechanics, in Fractals and Fractional Calculus in Continuum Mechanics, Carpinteri, A. and Mainardi, F. (eds), Springer, New York, 1997.
    • (1997) Fractals and Fractional Calculus in Continuum Mechanics
    • Mainardi, F.1
  • 32
    • 0242354999 scopus 로고    scopus 로고
    • Geometric and physical interpretation of fractional integration and fractional differentiation. Dedicated to the 60th anniversary of Prof. Francesco Mainardi
    • Podlubny, I.; Geometric and physical interpretation of fractional integration and fractional differentiation. Dedicated to the 60th anniversary of Prof. Francesco Mainardi. Fract. Calc. Appl. Anal., 5, 4 (2002), 367-386.
    • (2002) Fract. Calc. Appl. Anal. , vol.5 , Issue.4 , pp. 367-386
    • Podlubny, I.1
  • 33
    • 0036650890 scopus 로고    scopus 로고
    • Analogue realizations of fractional-order controllers. Fractional order calculus and its applications
    • Podlubny, I.; Petras, I.; Vinagre, B. M.; O'Leary, P.; Dorcak, L.; Analogue realizations of fractional-order controllers. Fractional order calculus and its applications. Nonlinear Dynam. 29, 1-4 (2002), 281-296.
    • (2002) Nonlinear Dynam. , vol.29 , Issue.1-4 , pp. 281-296
    • Podlubny, I.1    Petras, I.2    Vinagre, B.M.3    O'Leary, P.4    Dorcak, L.5
  • 34
    • 79952154262 scopus 로고
    • Oscillations of quasilinear systems with retardation
    • Rubanik, V. P.; Oscillations of quasilinear systems with retardation. Nauka, Moscow, 1969.
    • (1969) Nauka, Moscow
    • Rubanik, V.P.1
  • 37
  • 40
    • 23844442815 scopus 로고    scopus 로고
    • Existence of fractional differential equations
    • Yu, C.; Gao, G.; Existence of fractional differential equations. J. Math. Anal. Appl., 310, 1 (2005), 26-29.
    • (2005) J. Math. Anal. Appl. , vol.310 , Issue.1 , pp. 26-29
    • Yu, C.1    Gao, G.2
  • 41
    • 38949148649 scopus 로고    scopus 로고
    • Some results on a class of fractional functional differential equations
    • Yu, C.; Guozhu Gao, G.; Some results on a class of fractional functional differential equations, Commun. Appl. Nonlinear Anal., 11, 3 (2004), 67-75.
    • (2004) Commun. Appl. Nonlinear Anal. , vol.11 , Issue.3 , pp. 67-75
    • Yu, C.1    Guozhu Gao, G.2
  • 42
    • 38949212976 scopus 로고    scopus 로고
    • Some results of linear fractional order time-delay system
    • Zhang, X.; Some results of linear fractional order time-delay system Appl. Math. Comp, 197, 1 (2008), 407-411.
    • (2008) Appl. Math. Comp , vol.197 , Issue.1 , pp. 407-411
    • Zhang, X.1
  • 43
    • 33645152919 scopus 로고    scopus 로고
    • Positive solutions for boundary-value problems of nonlinear fractional differential equations
    • Zhang, S.; Positive solutions for boundary-value problems of nonlinear fractional differential equations. Electron. J. Diff. Eqns. 2006 (2006), No. 36, 1-12.
    • (2006) Electron. J. Diff. Eqns. , vol.2006 , Issue.36 , pp. 1-12
    • Zhang, S.1


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