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Year 2018, Volume: 2 Issue: 2, 74 - 84, 30.06.2018
https://doi.org/10.31197/atnaa.403249

Abstract

References

  • [1] A. A. Kilbas, H. M. Srivastava and J. J. Trijullo, Theory and applications of fractionaldifferential equations, Elsevier Science b. V, Amsterdam, (2006).[2] C. F. Li, X. N. Luo and Y. Zhou, Existence of positive solutions of the boundary value problemfor nonlinear fractional differential equations. Comput. Math. Appl. 59 (2010), 1363-1375.[3] D. Mozyrska, Z. Bartosiewicz, On Observability of Nonlinear Discrete-Time Fractional-OrderControl Systems New Trends in Nanotechnology and Fractional calculus Applications. (2010),305-312.1[4] D. Baleanu, H. Mohammadi, Sh. Rezapour, the existence of solutions for a nonlinear mixedproblem of singular fractional equations, Adv. Difference Equa. 2013 (2013), 12 pages.[5] J. R. Graef, L. Kong, Q. Kong and M. Wang, Uniqueness of positive solutions of fractionalboundary value problems with non-homogeneous integral boundary conditions, Fract. Calc.Appl. Anal. 15 (2012), 509-528.[6] J. R. Graef, L. Kong, Q. Kong, and M. Wang, Existence and uniqueness of solutions fora fractional boundary value problem with Dirichlet boundary condition, Electron. J. Qual.Theory Differ. Equ. 2013 No.55,11 pp.[7] K. H. Zhao, P. Gong, Existence of positive solutions for a class of higher-order Caputofractional differential equation. Qual. Theory Dyn. Syst. 14 (1) (2015), 157-171.[8] L. Zhang, B. Ahmed, G. Wang, R. B. Agarwal, Nonlinear fractional integro-differential equa-tions on unbounded domains in Banach space, J. Comput. Appl. Math. 249 (2013), 51-56.[9] L. Wang and X. Zhang, Positive solutions of m-point boundary value problems for a class ofnonlinear fractional differential equations. J. Appl. Math. Comput. 42 (2013), 387-399.

The Uniqueness of Positive Solution for Higher-Order Nonlinear Fractional Differential Equation With Fractional Multi-Point Boundary Conditions

Year 2018, Volume: 2 Issue: 2, 74 - 84, 30.06.2018
https://doi.org/10.31197/atnaa.403249

Abstract

 In this paper, we apply the iterative method to establish the existence of the positive solution for a type of nonlinear singular higher-order
fractional differential equation with fractional multi-point boundary conditions. Explicit iterative sequences are given to approximate the solutions and
the error estimations are also given. The result is illustrated with an example.

References

  • [1] A. A. Kilbas, H. M. Srivastava and J. J. Trijullo, Theory and applications of fractionaldifferential equations, Elsevier Science b. V, Amsterdam, (2006).[2] C. F. Li, X. N. Luo and Y. Zhou, Existence of positive solutions of the boundary value problemfor nonlinear fractional differential equations. Comput. Math. Appl. 59 (2010), 1363-1375.[3] D. Mozyrska, Z. Bartosiewicz, On Observability of Nonlinear Discrete-Time Fractional-OrderControl Systems New Trends in Nanotechnology and Fractional calculus Applications. (2010),305-312.1[4] D. Baleanu, H. Mohammadi, Sh. Rezapour, the existence of solutions for a nonlinear mixedproblem of singular fractional equations, Adv. Difference Equa. 2013 (2013), 12 pages.[5] J. R. Graef, L. Kong, Q. Kong and M. Wang, Uniqueness of positive solutions of fractionalboundary value problems with non-homogeneous integral boundary conditions, Fract. Calc.Appl. Anal. 15 (2012), 509-528.[6] J. R. Graef, L. Kong, Q. Kong, and M. Wang, Existence and uniqueness of solutions fora fractional boundary value problem with Dirichlet boundary condition, Electron. J. Qual.Theory Differ. Equ. 2013 No.55,11 pp.[7] K. H. Zhao, P. Gong, Existence of positive solutions for a class of higher-order Caputofractional differential equation. Qual. Theory Dyn. Syst. 14 (1) (2015), 157-171.[8] L. Zhang, B. Ahmed, G. Wang, R. B. Agarwal, Nonlinear fractional integro-differential equa-tions on unbounded domains in Banach space, J. Comput. Appl. Math. 249 (2013), 51-56.[9] L. Wang and X. Zhang, Positive solutions of m-point boundary value problems for a class ofnonlinear fractional differential equations. J. Appl. Math. Comput. 42 (2013), 387-399.
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Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Bouteraa Noureddine

Slimane Benaicha This is me

Publication Date June 30, 2018
Published in Issue Year 2018 Volume: 2 Issue: 2

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