EN
The Uniqueness of Positive Solution for Higher-Order Nonlinear Fractional Differential Equation With Fractional Multi-Point Boundary Conditions
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
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.
Details
Primary Language
English
Subjects
Mathematical Sciences
Journal Section
Research Article
Publication Date
June 30, 2018
Submission Date
March 8, 2018
Acceptance Date
April 20, 2018
Published in Issue
Year 2018 Volume: 2 Number: 2
APA
Noureddine, B., & Benaicha, S. (2018). The Uniqueness of Positive Solution for Higher-Order Nonlinear Fractional Differential Equation With Fractional Multi-Point Boundary Conditions. Advances in the Theory of Nonlinear Analysis and Its Application, 2(2), 74-84. https://doi.org/10.31197/atnaa.403249
AMA
1.Noureddine B, Benaicha S. The Uniqueness of Positive Solution for Higher-Order Nonlinear Fractional Differential Equation With Fractional Multi-Point Boundary Conditions. ATNAA. 2018;2(2):74-84. doi:10.31197/atnaa.403249
Chicago
Noureddine, Bouteraa, and Slimane Benaicha. 2018. “The Uniqueness of Positive Solution for Higher-Order Nonlinear Fractional Differential Equation With Fractional Multi-Point Boundary Conditions”. Advances in the Theory of Nonlinear Analysis and Its Application 2 (2): 74-84. https://doi.org/10.31197/atnaa.403249.
EndNote
Noureddine B, Benaicha S (June 1, 2018) The Uniqueness of Positive Solution for Higher-Order Nonlinear Fractional Differential Equation With Fractional Multi-Point Boundary Conditions. Advances in the Theory of Nonlinear Analysis and its Application 2 2 74–84.
IEEE
[1]B. Noureddine and S. Benaicha, “The Uniqueness of Positive Solution for Higher-Order Nonlinear Fractional Differential Equation With Fractional Multi-Point Boundary Conditions”, ATNAA, vol. 2, no. 2, pp. 74–84, June 2018, doi: 10.31197/atnaa.403249.
ISNAD
Noureddine, Bouteraa - Benaicha, Slimane. “The Uniqueness of Positive Solution for Higher-Order Nonlinear Fractional Differential Equation With Fractional Multi-Point Boundary Conditions”. Advances in the Theory of Nonlinear Analysis and its Application 2/2 (June 1, 2018): 74-84. https://doi.org/10.31197/atnaa.403249.
JAMA
1.Noureddine B, Benaicha S. The Uniqueness of Positive Solution for Higher-Order Nonlinear Fractional Differential Equation With Fractional Multi-Point Boundary Conditions. ATNAA. 2018;2:74–84.
MLA
Noureddine, Bouteraa, and Slimane Benaicha. “The Uniqueness of Positive Solution for Higher-Order Nonlinear Fractional Differential Equation With Fractional Multi-Point Boundary Conditions”. Advances in the Theory of Nonlinear Analysis and Its Application, vol. 2, no. 2, June 2018, pp. 74-84, doi:10.31197/atnaa.403249.
Vancouver
1.Bouteraa Noureddine, Slimane Benaicha. The Uniqueness of Positive Solution for Higher-Order Nonlinear Fractional Differential Equation With Fractional Multi-Point Boundary Conditions. ATNAA. 2018 Jun. 1;2(2):74-8. doi:10.31197/atnaa.403249
Cited By
Hilfer-Hadamard Fractional Differential Equations; Existence and Attractivity
Advances in the Theory of Nonlinear Analysis and its Application
https://doi.org/10.31197/atnaa.848928"A study of existence and multiplicity of positive solutions for nonlinear fractional differential equations with nonlocal boundary conditions"
Studia Universitatis Babes-Bolyai Matematica
https://doi.org/10.24193/subbmath.2021.2.12