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Volumn 29, Issue 1-2, 2009, Pages 125-135

A singular boundary value problem for nonlinear differential equations of fractional order

Author keywords

A priori estimate; Carath odory conditions; Leray Schauder Continuation Principle; Riemann Liouville derivative

Indexed keywords


EID: 58149470828     PISSN: 15985865     EISSN: None     Source Type: Journal    
DOI: 10.1007/s12190-008-0104-x     Document Type: Article
Times cited : (58)

References (23)
  • 1
    • 1242321329 scopus 로고    scopus 로고
    • The existence of a positive solution for a singular coupled system of nonlinear fractional differential equations
    • 1. C.Z. Bai J.X. Fang 2004 The existence of a positive solution for a singular coupled system of nonlinear fractional differential equations Appl. Math. Comput. 150 611 621 1061.34001 10.1016/S0096-3003(03)00294-7 2039662 Bai, C.Z., Fang, J.X.: The existence of a positive solution for a singular coupled system of nonlinear fractional differential equations. Appl. Math. Comput. 150, 611–621 (2004)
    • (2004) Appl. Math. Comput. , vol.150 , pp. 611-621
    • Bai, C.Z.1    Fang, J.X.2
  • 2
    • 25144460994 scopus 로고    scopus 로고
    • Positive solutions for boundary value problem of nonlinear fractional differential equation
    • 2. Z. Bai H. Lü 2005 Positive solutions for boundary value problem of nonlinear fractional differential equation J. Math. Anal. Appl. 311 495 505 1079.34048 10.1016/j.jmaa.2005.02.052 2168413 Bai, Z., Lü, H.: Positive solutions for boundary value problem of nonlinear fractional differential equation. J. Math. Anal. Appl. 311, 495–505 (2005)
    • (2005) J. Math. Anal. Appl. , vol.311 , pp. 495-505
    • Bai, Z.1    Lü, H.2
  • 3
    • 34848916710 scopus 로고    scopus 로고
    • Existence results for fractional order functional differential equations with infinite delay
    • 3. M. Benchohra J. Henderson S.K. Ntoyuas A. Quahab 2008 Existence results for fractional order functional differential equations with infinite delay J. Math. Anal. Appl. 338 1340 1350 05242627 10.1016/j.jmaa.2007.06.021 2386501 Benchohra, M., Henderson, J., Ntoyuas, S.K., Quahab, A.: Existence results for fractional order functional differential equations with infinite delay. J. Math. Anal. Appl. 338, 1340–1350 (2008)
    • (2008) J. Math. Anal. Appl. , vol.338 , pp. 1340-1350
    • Benchohra, M.1    Henderson, J.2    Ntoyuas, S.K.3    Quahab, A.4
  • 4
    • 10844262723 scopus 로고    scopus 로고
    • Positive solutions of a system of non-autonomous fractional differential equations
    • 4. V. Daftardar-Gejji 2005 Positive solutions of a system of non-autonomous fractional differential equations J. Math. Anal. Appl. 302 56 64 1064.34004 10.1016/j.jmaa.2004.08.007 2106546 Daftardar-Gejji, V.: Positive solutions of a system of non-autonomous fractional differential equations. J. Math. Anal. Appl. 302, 56–64 (2005)
    • (2005) J. Math. Anal. Appl. , vol.302 , pp. 56-64
    • Daftardar-Gejji, V.1
  • 5
    • 0030528474 scopus 로고    scopus 로고
    • Existence and uniqueness for a nonlinear fractional differential equation
    • 5. D. Delbosco L. Rodino 1996 Existence and uniqueness for a nonlinear fractional differential equation J. Math. Anal. Appl. 204 609 625 0881.34005 10.1006/jmaa.1996.0456 1421467 Delbosco, D., Rodino, L.: Existence and uniqueness for a nonlinear fractional differential equation. J. Math. Anal. Appl. 204, 609–625 (1996)
    • (1996) J. Math. Anal. Appl. , vol.204 , pp. 609-625
    • Delbosco, D.1    Rodino, L.2
  • 6
    • 85121068467 scopus 로고    scopus 로고
    • 6. K. Diethelm A.D. Freed 1999 On the solution of nolinear fractional order differential equations used in the modelling of viscoplasticity F. Keil W. Mackens H. Voss Scientific Computing in Chemical Engineering II—Computational Fluid Dynamics and Molecular Properties Springer Heidelberg 217 224 Diethelm, K., Freed, A.D.: On the solution of nolinear fractional order differential equations used in the modelling of viscoplasticity. In: Keil, F., Mackens, W., Voss, H. (eds.) Scientific Computing in Chemical Engineering II—Computational Fluid Dynamics and Molecular Properties, pp. 217–224. Springer, Heidelberg (1999)
  • 7
    • 2942756137 scopus 로고    scopus 로고
    • On the functional integral equations of mixed type and integro-differential equations of fractional orders
    • 7. W.G. El-Sayed A.M.A. El-Sayed 2004 On the functional integral equations of mixed type and integro-differential equations of fractional orders Appl. Math. Comput. 154 461 467 1061.45004 10.1016/S0096-3003(03)00727-6 2111383 El-Sayed, W.G., El-Sayed, A.M.A.: On the functional integral equations of mixed type and integro-differential equations of fractional orders. Appl. Math. Comput. 154, 461–467 (2004)
    • (2004) Appl. Math. Comput. , vol.154 , pp. 461-467
    • El-Sayed, W.G.1    El-Sayed, A.M.A.2
  • 8
    • 21344473946 scopus 로고    scopus 로고
    • A Dirichlet-Neumann m-point BVP with a p-Laplacian-like operator
    • 8. M. García-Huidobro C.P. Gupta R. Manásevich 2005 A Dirichlet-Neumann m-point BVP with a p-Laplacian-like operator Nonlinear Anal. 62 6 1067 1089 1082.34011 10.1016/j.na.2005.04.020 2152998 García-Huidobro, M., Gupta, C.P., Manásevich, R.: A Dirichlet-Neumann m-point BVP with a p-Laplacian-like operator. Nonlinear Anal. 62 (6), 1067–1089 (2005)
    • (2005) Nonlinear Anal. , vol.62 , Issue.6 , pp. 1067-1089
    • García-Huidobro, M.1    Gupta, C.P.2    Manásevich, R.3
  • 9
    • 29244462825 scopus 로고    scopus 로고
    • A non-resonant multi-point boundary value problem of Neumann-Dirichlet type for a p-Laplacian type operator
    • 9. C.P. Gupta 2004 A non-resonant multi-point boundary value problem of Neumann-Dirichlet type for a p-Laplacian type operator Dyn. Syst. Appl. 4 439 442 Gupta, C.P.: A non-resonant multi-point boundary value problem of Neumann-Dirichlet type for a p-Laplacian type operator. Dyn. Syst. Appl. 4, 439–442 (2004)
    • (2004) Dyn. Syst. Appl. , vol.4 , pp. 439-442
    • Gupta, C.P.1
  • 10
    • 13844295441 scopus 로고    scopus 로고
    • A priori estimates for the existence of a solution for a multi-point boundary value problem
    • 10. C.P. Gupta S. Trofimchuk 2000 A priori estimates for the existence of a solution for a multi-point boundary value problem J. Inequal. Appl. 5 4 351 365 0967.34006 10.1155/S1025583400000187 1784983 Gupta, C.P., Trofimchuk, S.: A priori estimates for the existence of a solution for a multi-point boundary value problem. J. Inequal. Appl. 5 (4), 351–365 (2000)
    • (2000) J. Inequal. Appl. , vol.5 , Issue.4 , pp. 351-365
    • Gupta, C.P.1    Trofimchuk, S.2
  • 11
    • 50349092768 scopus 로고    scopus 로고
    • Existence of the mild solution for fractional semilinear initial value problems
    • 11. O.K. Jaradat A. Al-Omari S. Momani 2007 Existence of the mild solution for fractional semilinear initial value problems Nonlinear Anal. 10.1016/j.na.2007.09.008 Jaradat, O.K., Al-Omari, A., Momani, S.: Existence of the mild solution for fractional semilinear initial value problems. Nonlinear Anal. (2007). doi: 10.1016/j.na.2007.09.008
    • (2007) Nonlinear Anal.
    • Jaradat, O.K.1    Al-Omari, A.2    Momani, S.3
  • 12
    • 77956684069 scopus 로고    scopus 로고
    • Theory and Applications of Fractional Differential Equations
    • 12. A.A. Kilbas H.M. Srivastava J.J. Trujillo 2006 Theory and Applications of Fractional Differential Equations North Holland Mathematics Studies 204 Elsevier Amsterdam 1092.45003 10.1016/S0304-0208(06)80001-0 Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. North Holland Mathematics Studies, vol. 204. Elsevier, Amsterdam (2006)
    • (2006)
    • Kilbas, A.A.1    Srivastava, H.M.2    Trujillo, J.J.3
  • 13
    • 0003654359 scopus 로고
    • Generalized Fractional Calculus and Applications
    • 13. V.S. Kiryakova 1993 Generalized Fractional Calculus and Applications Chapman & Hall London Kiryakova, V.S.: Generalized Fractional Calculus and Applications. Chapman & Hall, London (1993)
    • (1993)
    • Kiryakova, V.S.1
  • 14
    • 84951106764 scopus 로고
    • Topological Methods in the Theory of Nonlinear Integral Equations (trans: Armstrong, A.H.)
    • 14. M.A. Krasnosel’skiĭ 1964 Topological Methods in the Theory of Nonlinear Integral Equations (trans: Armstrong, A.H.) Pergamon Elmsford Krasnosel’skiĭ, M.A.: Topological Methods in the Theory of Nonlinear Integral Equations (trans: Armstrong, A.H.). Pergamon, Elmsford (1964)
    • (1964)
    • Krasnosel’skiĭ, M.A.1
  • 15
    • 51349139941 scopus 로고    scopus 로고
    • Theory of fractional functional differential equations
    • 15. V. Lakshmikantham 2007 Theory of fractional functional differential equations Nonlinear Anal. 10.1016/j.na.2007.09.025 Lakshmikantham, V.: Theory of fractional functional differential equations. Nonlinear Anal. (2007). doi: 10.1016/j.na.2007.09.025
    • (2007) Nonlinear Anal.
    • Lakshmikantham, V.1
  • 16
    • 53949111458 scopus 로고    scopus 로고
    • Basic theory of fractional differential equations
    • 16. V. Lakshmikantham A.S. Vatsala 2007 Basic theory of fractional differential equations Nonlinear Anal. 10.1016/j.na/207.08.042 Lakshmikantham, V., Vatsala, A.S.: Basic theory of fractional differential equations. Nonlinear Anal. (2007). doi: 10.1016/j.na/207.08.042
    • (2007) Nonlinear Anal.
    • Lakshmikantham, V.1    Vatsala, A.S.2
  • 17
    • 0000394603 scopus 로고
    • Multiple positive fixed points of operators on ordered Banach spaces
    • 17. R.W. Leggett L.R. Williams 1979 Multiple positive fixed points of operators on ordered Banach spaces Indiana Univ. Math. J. 28 673 688 0421.47033 10.1512/iumj.1979.28.28046 542951 Leggett, R.W., Williams, L.R.: Multiple positive fixed points of operators on ordered Banach spaces. Indiana Univ. Math. J. 28, 673–688 (1979)
    • (1979) Indiana Univ. Math. J. , vol.28 , pp. 673-688
    • Leggett, R.W.1    Williams, L.R.2
  • 18
    • 34247212711 scopus 로고    scopus 로고
    • Remarks on fractional derivatives
    • 18. C. Li W. Deng 2007 Remarks on fractional derivatives Appl. Math. Comput. 187 777 784 1125.26009 10.1016/j.amc.2006.08.163 2323083 Li, C., Deng, W.: Remarks on fractional derivatives. Appl. Math. Comput. 187, 777–784 (2007)
    • (2007) Appl. Math. Comput. , vol.187 , pp. 777-784
    • Li, C.1    Deng, W.2
  • 19
    • 10144224236 scopus 로고    scopus 로고
    • Solvability of singular second order m-point boundary value problems
    • 19. R. Ma D. O’Regan 2005 Solvability of singular second order m-point boundary value problems J. Math. Anal. Appl. 301 124 134 1062.34018 10.1016/j.jmaa.2004.07.009 2105925 Ma, R., O’Regan, D.: Solvability of singular second order m-point boundary value problems. J. Math. Anal. Appl. 301, 124–134 (2005)
    • (2005) J. Math. Anal. Appl. , vol.301 , pp. 124-134
    • Ma, R.1    O’Regan, D.2
  • 20
    • 0003797958 scopus 로고    scopus 로고
    • Fractional Differential Equations
    • 20. I. Podlubny 1999 Fractional Differential Equations Mathematics in Sciences and Applications 198 Academic Press San Diego 0924.34008 Podlubny, I.: Fractional Differential Equations. Mathematics in Sciences and Applications, vol. 198. Academic Press, San Diego (1999)
    • (1999)
    • Podlubny, I.1
  • 21
    • 84885710343 scopus 로고    scopus 로고
    • Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering
    • 21. J. Sabatier O.P. Agrawal J.A. Tenreiro-Machado 2007 Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering Springer New York 1116.00014 Sabatier, J., Agrawal, O.P., Tenreiro-Machado, J.A.: Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering. Springer, New York (2007)
    • (2007)
    • Sabatier, J.1    Agrawal, O.P.2    Tenreiro-Machado, J.A.3
  • 22
    • 0003598080 scopus 로고
    • Fractional Integral and Derivatives (Theory and Applications)
    • 22. S.G. Samko A.A. Kilbas O.I. Mirichev 1993 Fractional Integral and Derivatives (Theory and Applications) Gordon and Breach New York Samko, S.G., Kilbas, A.A., Mirichev, O.I.: Fractional Integral and Derivatives (Theory and Applications). Gordon and Breach, New York (1993)
    • (1993)
    • Samko, S.G.1    Kilbas, A.A.2    Mirichev, O.I.3
  • 23
    • 0003678750 scopus 로고
    • Nonlinear Functional Analysis and Applications, I: Fixed Point Theorems
    • 23. E. Zeidler 1986 Nonlinear Functional Analysis and Applications, I: Fixed Point Theorems Springer New York 0583.47050 Zeidler, E.: Nonlinear Functional Analysis and Applications, I: Fixed Point Theorems. Springer, New York (1986)
    • (1986)
    • Zeidler, E.1


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