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On a System of Fractional Differential Equations with Coupled Integral Boundary Conditions

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Abstract

We investigate the existence and multiplicity of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations, subject to coupled integral boundary conditions. The nonsingular and singular cases are studied.

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References

  1. H. Amann, Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces. SIAM Review 18 (1976), 620–709.

    Article  MathSciNet  Google Scholar 

  2. S. Das, Functional Fractional Calculus for System Identification and Controls. Springer, New York (2008).

    MATH  Google Scholar 

  3. J.R. Graef, L. Kong, Q. Kong, M. Wang, Uniqueness of positive solutions of fractional boundary value problems with nonhomogeneous integral boundary conditions. Fract. Calc. Appl. Anal. 15, No 3 (2012), 509–528; DOI:10.2478/s13540-012-0036-x; http://link.springer.com/article/10.2478/s13540-012-0036-x.

    Article  MathSciNet  Google Scholar 

  4. D. Guo, V. Lakshmikantham, Nonlinear Problems in Abstract Cones. Academic Press, New York (1988).

    MATH  Google Scholar 

  5. J. Henderson, R. Luca, Positive solutions for a system of nonlocal fractional boundary value problems. Fract. Calc. Appl. Anal. 16, No 4 (2013), 985–1008 (2013); DOI:10.2478/s13540-013-0061-4; http://link.springer.com/article/10.2478/s13540-013-0061-4.

    Article  MathSciNet  Google Scholar 

  6. J. Henderson, R. Luca, Existence and multiplicity of positive solutions for a system of fractional boundary value problems. Bound. Value Prob. 2014 (2014), # 60, 17 pp.; DOI:10.1186/1687-2770-2014-60.

    Article  MathSciNet  Google Scholar 

  7. J. Henderson, R. Luca, Positive solutions for a system of fractional differential equations with coupled integral boundary conditions. Appl. Math. Comput. 249 (2014), 182–197; DOI:10.1016/j.amc.2014.10.028.

    MathSciNet  MATH  Google Scholar 

  8. A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, 204, Elsevier Science B.V., Amsterdam (2006).

    MATH  Google Scholar 

  9. R. Luca, A. Tudorache, Positive solutions to a system of semipositone fractional boundary value problems. Adv. Difference Equ. 2014 (2014), # 179, 11 pp.; DOI:10.1186/1687-1847-2014-179.

    Article  MathSciNet  Google Scholar 

  10. I. Podlubny, Fractional Differential Equations. Academic Press, San Diego (1999).

    MATH  Google Scholar 

  11. J. Sabatier, O.P. Agrawal, J.A.T. Machado (Eds.), Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering. Springer, Dordrecht (2007).

    Book  Google Scholar 

  12. S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives. Theory and Applications. Gordon and Breach, Yverdon (1993).

    MATH  Google Scholar 

  13. C. Yuan, D. Jiang, D. O’Regan, R.P. Agarwal, Multiple positive solutions to systems of nonlinear semipositone fractional differential equations with coupled boundary conditions. Electron. J. Qualit. Theory Differ. Equ. 2012, No 13 (2012), 17 pp.

    Article  MathSciNet  Google Scholar 

  14. Y. Zhou, Y. Xu, Positive solutions of three-point boundary value problems for systems of nonlinear second order ordinary differential equations. J. Math. Anal. Appl. 320 (2006), 578–590; DOI:10.1016/j.jmaa.2005.07.014.

    Article  MathSciNet  Google Scholar 

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Correspondence to Johnny Henderson.

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Henderson, J., Luca, R. & Tudorache, A. On a System of Fractional Differential Equations with Coupled Integral Boundary Conditions. FCAA 18, 361–386 (2015). https://doi.org/10.1515/fca-2015-0024

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  • DOI: https://doi.org/10.1515/fca-2015-0024

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