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Volumn 2013, Issue , 2013, Pages

Existence results for a class of fractional differential equations with periodic boundary value conditions and with delay

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EID: 84885447798     PISSN: 10853375     EISSN: 16870409     Source Type: Journal    
DOI: 10.1155/2013/176180     Document Type: Article
Times cited : (5)

References (38)
  • 6
    • 33745869026 scopus 로고    scopus 로고
    • Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives
    • DOI 10.1007/s00397-005-0043-5
    • Heymans N., Podlubny I., Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives. Rheologica Acta 2006 45 5 765 771 2-s2.0-33745869026 10.1007/s00397-005-0043-5 (Pubitemid 44027219)
    • (2006) Rheologica Acta , vol.45 , Issue.5 , pp. 765-771
    • Heymans, N.1    Podlubny, I.2
  • 8
    • 0242354999 scopus 로고    scopus 로고
    • Geometric and physical interpretation of fractional integration and fractional differentiation
    • Dedicated to the 60th anniversary of Prof. Francesco Mainardi MR1967839
    • Podlubny I., Geometric and physical interpretation of fractional integration and fractional differentiation. Fractional Calculus & Applied Analysis 2002 5 4 367 386. Dedicated to the 60th anniversary of Prof. Francesco Mainardi MR1967839
    • (2002) Fractional Calculus & Applied Analysis , vol.5 , Issue.4 , pp. 367-386
    • Podlubny, I.1
  • 9
    • 0036650890 scopus 로고    scopus 로고
    • Analogue realizations of fractional-order controllers
    • DOI 10.1023/A:1016556604320, Fractional Order Calculus and Its Applications
    • Podlubny I., Petráš I., Vinagre B. M., O'Leary P., Dorčák L., Analogue realizations of fractional-order controllers. Fractional order calculus and its applications. Nonlinear Dynamics 2002 29 1-4 281 296 10.1023/A:1016556604320 MR1926477 (Pubitemid 34945402)
    • (2002) Nonlinear Dynamics , 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
  • 12
    • 84891735830 scopus 로고    scopus 로고
    • On development of fractional calculus during the last fifty years
    • New York, NY, USA Springer
    • Machado J. T., Galhano A. M., Trujillo J. J., On development of fractional calculus during the last fifty years. Scientometrics 2013 New York, NY, USA Springer
    • (2013) Scientometrics
    • Machado, J.T.1    Galhano, A.M.2    Trujillo, J.J.3
  • 13
    • 0011642556 scopus 로고
    • Fractional order differential equation
    • El-Sayed A., Fractional order differential equation. Kyungpook Mathematical Journal 1988 28 2 18 22
    • (1988) Kyungpook Mathematical Journal , vol.28 , Issue.2 , pp. 18-22
    • El-Sayed, A.1
  • 14
    • 44049116967 scopus 로고
    • On the fractional differential equations
    • 10.1016/0096-3003(92)90024-U MR1162161
    • El-Sayed A., On the fractional differential equations. Applied Mathematics and Computation 1992 49 2-3 205 213 10.1016/0096-3003(92)90024-U MR1162161
    • (1992) Applied Mathematics and Computation , vol.49 , Issue.2-3 , pp. 205-213
    • El-Sayed, A.1
  • 15
    • 0032115069 scopus 로고    scopus 로고
    • Nonlinear functional differential equations of arbitrary orders
    • PII S0362546X97005257
    • El-Sayed A., Nonlinear functional-differential equations of arbitrary orders. Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal. Series A: Theory and Methods 1998 33 2 181 186 10.1016/S0362-546X(97)00525-7 MR1621105 (Pubitemid 128403304)
    • (1998) Nonlinear Analysis, Theory, Methods and Applications , vol.33 , Issue.2 , pp. 181-186
    • El-Sayed, A.M.A.1
  • 16
    • 74149092568 scopus 로고    scopus 로고
    • Existence of fractional neutral functional differential equations
    • 10.1016/j.camwa.2009.05.010 MR2579474
    • Agarwal R. P., Zhou Y., He Y., Existence of fractional neutral functional differential equations. Computers & Mathematics with Applications 2010 59 3 1095 1100 10.1016/j.camwa.2009.05.010 MR2579474
    • (2010) Computers & Mathematics with Applications , vol.59 , Issue.3 , pp. 1095-1100
    • Agarwal, R.P.1    Zhou, Y.2    He, Y.3
  • 17
    • 2442548776 scopus 로고    scopus 로고
    • Analysis of a system of fractional differential equations
    • DOI 10.1016/j.jmaa.2004.01.013
    • Daftardar-Gejji V., Babakhani A., Analysis of a system of fractional differential equations. Journal of Mathematical Analysis and Applications 2004 293 2 511 522 10.1016/j.jmaa.2004.01.013 MR2053894 (Pubitemid 38613236)
    • (2004) Journal of Mathematical Analysis and Applications , vol.293 , Issue.2 , pp. 511-522
    • Daftardar-Gejji, V.1    Babakhani, A.2
  • 18
    • 84877623455 scopus 로고    scopus 로고
    • Existence of solutions for impulsive differential models on half lines involving Caputo fractional derivatives
    • MR3055036 10.1016/j.cnsns.2013.02.003
    • Liu Y., Existence of solutions for impulsive differential models on half lines involving Caputo fractional derivatives. Communications in Nonlinear Science and Numerical Simulation 2013 18 10 2604 2625 MR3055036 10.1016/j.cnsns.2013.02.003
    • (2013) Communications in Nonlinear Science and Numerical Simulation , vol.18 , Issue.10 , pp. 2604-2625
    • Liu, Y.1
  • 19
    • 0030528474 scopus 로고    scopus 로고
    • Existence and uniqueness for a nonlinear fractional differential equation
    • DOI 10.1006/jmaa.1996.0456
    • Delbosco D., Rodino L., Existence and uniqueness for a nonlinear fractional differential equation. Journal of Mathematical Analysis and Applications 1996 204 2 609 625 10.1006/jmaa.1996.0456 MR1421467 (Pubitemid 126163548)
    • (1996) Journal of Mathematical Analysis and Applications , vol.204 , Issue.2 , pp. 609-625
    • Delbosco, D.1    Rodino, L.2
  • 20
    • 77950188013 scopus 로고    scopus 로고
    • Existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations
    • 10.1016/j.aml.2010.02.007 MR2609797
    • Deng J., Ma L., Existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations. Applied Mathematics Letters 2010 23 6 676 680 10.1016/j.aml.2010.02.007 MR2609797
    • (2010) Applied Mathematics Letters , vol.23 , Issue.6 , pp. 676-680
    • Deng, J.1    Ma, L.2
  • 21
    • 0037081673 scopus 로고    scopus 로고
    • Analysis of fractional differential equations
    • 10.1006/jmaa.2000.7194 MR1876137
    • Diethelm K., Ford N. J., Analysis of fractional differential equations. Journal of Mathematical Analysis and Applications 2002 265 2 229 248 10.1006/jmaa.2000.7194 MR1876137
    • (2002) Journal of Mathematical Analysis and Applications , vol.265 , Issue.2 , pp. 229-248
    • Diethelm, K.1    Ford, N.J.2
  • 22
    • 33947244499 scopus 로고    scopus 로고
    • On the fractional-order logistic equation
    • DOI 10.1016/j.aml.2006.08.013, PII S0893965906002709
    • El-Sayed A., El-Mesiry A., El-Saka H., On the fractional-order logistic equation. Applied Mathematics Letters 2007 20 7 817 823 10.1016/j.aml.2006.08. 013 MR2314715 (Pubitemid 46428071)
    • (2007) Applied Mathematics Letters , vol.20 , Issue.7 , pp. 817-823
    • El-Sayed, A.M.A.1    El-Mesiry, A.E.M.2    El-Saka, H.A.A.3
  • 23
    • 34147158309 scopus 로고    scopus 로고
    • Long time behavior for a nonlinear fractional model
    • 10.1016/j.jmaa.2006.10.027 MR2319674
    • Furati K. M., Tatar N.-E., Long time behavior for a nonlinear fractional model. Journal of Mathematical Analysis and Applications 2007 332 1 441 454 10.1016/j.jmaa.2006.10.027 MR2319674
    • (2007) Journal of Mathematical Analysis and Applications , vol.332 , Issue.1 , pp. 441-454
    • Furati, K.M.1    Tatar, N.-E.2
  • 24
    • 8844229377 scopus 로고
    • Local and global existence theorems on differential equations of non-integer order
    • MR1330572
    • Hadid S. B., Local and global existence theorems on differential equations of non-integer order. Journal of Fractional Calculus 1995 7 101 105 MR1330572
    • (1995) Journal of Fractional Calculus , vol.7 , pp. 101-105
    • Hadid, S.B.1
  • 25
    • 17844379086 scopus 로고    scopus 로고
    • On the existence of maximal and minimal solutions of differential equations of non-integer order
    • MR1389417
    • Hadid S., Masaedeh B., Momani S., On the existence of maximal and minimal solutions of differential equations of non-integer order. Journal of Fractional Calculus 1996 9 41 44 MR1389417
    • (1996) Journal of Fractional Calculus , vol.9 , pp. 41-44
    • Hadid, S.1    Masaedeh, B.2    Momani, S.3
  • 26
    • 34249295169 scopus 로고    scopus 로고
    • On the existence and uniqueness of solutions of a class of fractional differential equations
    • 10.1016/j.jmaa.2006.12.036 MR2332533
    • Ibrahim R. W., Momani S., On the existence and uniqueness of solutions of a class of fractional differential equations. Journal of Mathematical Analysis and Applications 2007 334 1 1 10 10.1016/j.jmaa.2006.12.036 MR2332533
    • (2007) Journal of Mathematical Analysis and Applications , vol.334 , Issue.1 , pp. 1-10
    • Ibrahim, R.W.1    Momani, S.2
  • 28
    • 34848916710 scopus 로고    scopus 로고
    • Existence results for fractional order functional differential equations with infinite delay
    • 10.1016/j.jmaa.2007.06.021 MR2386501
    • Benchohra M., Henderson J., Ntouyas S. K., Ouahab A., Existence results for fractional order functional differential equations with infinite delay. Journal of Mathematical Analysis and Applications 2008 338 2 1340 1350 10.1016/j.jmaa.2007.06.021 MR2386501
    • (2008) Journal of Mathematical Analysis and Applications , vol.338 , Issue.2 , pp. 1340-1350
    • Benchohra, M.1    Henderson, J.2    Ntouyas, S.K.3    Ouahab, A.4
  • 29
    • 70249121999 scopus 로고    scopus 로고
    • Existence of periodic solution for a nonlinear fractional differential equation
    • 324561 10.1155/2009/324561 MR2525590
    • Belmekki M., Nieto J. J., Rodríguez-López R., Existence of periodic solution for a nonlinear fractional differential equation. Boundary Value Problems 2009 2009 18 324561 10.1155/2009/324561 MR2525590
    • (2009) Boundary Value Problems , vol.2009 , pp. 18
    • Belmekki, M.1    Nieto, J.J.2    Rodríguez-López, R.3
  • 30
    • 79952143093 scopus 로고    scopus 로고
    • Existence of solutions to fractional order ordinary and delay differential equations and applications
    • MR2764326
    • Abbas S., Existence of solutions to fractional order ordinary and delay differential equations and applications. Electronic Journal of Differential Equations 2011 2011 09 1 11 MR2764326
    • (2011) Electronic Journal of Differential Equations , vol.2011 , Issue.9 , pp. 1-11
    • Abbas, S.1
  • 31
    • 37349014877 scopus 로고    scopus 로고
    • Theory of fractional differential inequalities and applications
    • MR2368191
    • Lakshmikantham V., Vatsala A. S., Theory of fractional differential inequalities and applications. Communications in Applied Analysis 2007 11 3-4 395 402 MR2368191
    • (2007) Communications in Applied Analysis , vol.11 , Issue.3-4 , pp. 395-402
    • Lakshmikantham, V.1    Vatsala, A.S.2
  • 32
    • 23844442815 scopus 로고    scopus 로고
    • Existence of fractional differential equations
    • DOI 10.1016/j.jmaa.2004.12.015, PII S0022247X0401039X
    • Yu C., Gao G., Existence of fractional differential equations. Journal of Mathematical Analysis and Applications 2005 310 1 26 29 10.1016/j.jmaa.2004.12. 015 MR2160670 (Pubitemid 41149444)
    • (2005) Journal of Mathematical Analysis and Applications , vol.310 , Issue.1 , pp. 26-29
    • Yu, C.1    Gao, G.2
  • 33
    • 78049476732 scopus 로고    scopus 로고
    • Pseudo almost automorphic solutions of fractional order neutral differential equation
    • 10.1007/s00233-010-9227-0 MR2735657
    • Abbas S., Pseudo almost automorphic solutions of fractional order neutral differential equation. Semigroup Forum 2010 81 3 393 404 10.1007/s00233-010- 9227-0 MR2735657
    • (2010) Semigroup Forum , vol.81 , Issue.3 , pp. 393-404
    • Abbas, S.1
  • 34
    • 71549167605 scopus 로고    scopus 로고
    • Boundary value problems for fractional differential equations
    • 10.1007/s10440-008-9356-6 MR2572663
    • Agarwal R. P., Benchohra M., Hamani S., Boundary value problems for fractional differential equations. Georgian Mathematical Journal 2009 16 3 401 411 10.1007/s10440-008-9356-6 MR2572663
    • (2009) Georgian Mathematical Journal , vol.16 , Issue.3 , pp. 401-411
    • Agarwal, R.P.1    Benchohra, M.2    Hamani, S.3
  • 35
    • 78149410275 scopus 로고    scopus 로고
    • A new approach to the theory of functional integral equations of fractional order
    • 10.1016/j.jmaa.2010.09.004 MR2735528
    • Banas J., Zajcac T., A new approach to the theory of functional integral equations of fractional order. Journal of Mathematical Analysis and Applications 2011 375 2 375 387 10.1016/j.jmaa.2010.09.004 MR2735528
    • (2011) Journal of Mathematical Analysis and Applications , vol.375 , Issue.2 , pp. 375-387
    • Banas, J.1    Zajcac, T.2
  • 36
    • 0037457777 scopus 로고    scopus 로고
    • The problem of the initial conditions and their physical meaning in linear differential equations of fractional order
    • 10.1016/S0096-3003(02)00323-5 MR1984230
    • Giannantoni C., The problem of the initial conditions and their physical meaning in linear differential equations of fractional order. Applied Mathematics and Computation 2003 141 1 87 102 10.1016/S0096-3003(02)00323-5 MR1984230
    • (2003) Applied Mathematics and Computation , vol.141 , Issue.1 , pp. 87-102
    • Giannantoni, C.1
  • 37
    • 33745869026 scopus 로고    scopus 로고
    • Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives
    • DOI 10.1007/s00397-005-0043-5
    • Heymans N., Podlubny I., Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives. Rheologica Acta 2006 45 5 765 771 2-s2.0-33745869026 10.1007/s00397-005-0043-5 (Pubitemid 44027219)
    • (2006) Rheologica Acta , vol.45 , Issue.5 , pp. 765-771
    • Heymans, N.1    Podlubny, I.2


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