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

Year 2018, , 74 - 84, 30.06.2018

Bouteraa Noureddine , Slimane Benaicha

https://doi.org/10.31197/atnaa.403249

Cited By: 4

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.

Keywords

Positive Solution, Uniqueness, Iterative sequence

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.