Existence of positive solutions of Hadamard fractional defferential equations with integral boundary conditions
DOI:
https://doi.org/10.5269/bspm.44099Abstract
In this paper, We study the existence of positive solutions for Hadamard fractional differential equations with integral conditions. We employ Avery-Peterson fixed point theorem and properties of Green's function to show the existence of positive solutions of our problem. Furthermore, we present an example to illustrate our main result.
References
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12. S. Zhang, Positive solutions for boundary value problems of linear fractional differential equations, Electr. J. Differ. Equ., 36 (2006), 1-12.
13. L. Zhang, Existence of positive solutions for a class of fractional differential equations with integral boundary conditions, Acta. Math. Appl. Sin., 38 (2015), 423-433.
14. L. Zhang, Z. Xuan, Multiple positive solutions for a second-order boundary value problem with integral boundary conditions, Bound. Value Probl., 2016 (2016), 8 pages.
2. B. Ahmad, J. J. Nieto, Existence results for nonlinear boundary value problems of fractional integrodifferential equations with integral boundary conditions, Bound. value probl., 2009 (2009), 11 pages.
3. B. Ahmad, S. K. Ntouyas, Existence and uniqueness of solutions for Caputo-Hadamard sequential fractional order neutral functional differential equations, Electronic Journal of Differential Equations, Vol. 2017 (2017), No. 36, pp. 1-11.
4. R. I. Avery, A. C. Peterson, Three positive fixed points of nonlinear operators on ordere d Banach spaces , Comput. Math. Appl., 42 (2001), 311-322.
5. A. Cabada, G. Wang, Positive solutions of nonlinear fractional differential equations with integral boundary value conditions, J. Maths. Anal. Appl. 389(2012) 403-411.
6. M. Jia, X. Liu, Three nonnegative solutions for fractional differential equtaions with integral boundary conditions, Comput. Math. Appl., 62 (2011), 1405-1412.
7. Kilbas, H. M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations. North-Holland Math. Stud., 204 (2006).
8. W. Sun, Y. Wang, Multiple positive solutions of nonlinear fractional differential equations with integral boundary value conditions, Fract. Calc. Appl. Anal., 17 (2014), 605-616.
9. Y. Wang, S.Liang, Q. Wang, Multiple positive solutions of fractional-order boundary value problem with integral boundary conditions, J. Nonlinear Sci. Appl., 10 (2017), 6333-6343.
10. Y. Wang, W. Ge, Multiple positive solutions for multipoint boundary value problems with one-dimensional p-Laplacian, J. Math. Anal. Appl., 327 (2007), 1381-1395.
11. Z. Wei, C. Pang, Y. Ding, Positive solutions of singular Caputo fractional differential equations with integral boundary conditions , Commun. Nonlinear Sci. Numer. Simulat., 17 (2012), 3148-3160.
12. S. Zhang, Positive solutions for boundary value problems of linear fractional differential equations, Electr. J. Differ. Equ., 36 (2006), 1-12.
13. L. Zhang, Existence of positive solutions for a class of fractional differential equations with integral boundary conditions, Acta. Math. Appl. Sin., 38 (2015), 423-433.
14. L. Zhang, Z. Xuan, Multiple positive solutions for a second-order boundary value problem with integral boundary conditions, Bound. Value Probl., 2016 (2016), 8 pages.
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2021-12-16
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