The unique solution of some operator equations via fractional differential equations
DOI:
https://doi.org/10.5269/bspm.45296Abstract
In this paper we consider the existence and uniqueness of positive solutions to the following operator equation in an ordered Banach space $E$
$$A(x,x)+B(x,x)=x,~x\in P,$$
where $P$ is a cone in $E$. We study an application for fractional differential equations.
References
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3. Kilbas A A, Srivastava H M, Trujillo, j j: Theory and applications of fractional differential equations. North-Holland Mathematics Studies. 204, 7-10(2006).
4. Liu. L, Zhang. X, Jiang. J, Wu. Y : The unique solution of a class of sum mixed monotone operator equations and its application to fractional boundary value problems J. Nonlinear Sci. Appl. 9 (2016), 2943-2958. https://doi.org/10.22436/jnsa.009.05.87
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2. Guo D: Fixed points of mixed monotone operators with application. Appl. Anal. 34, 215-224(1988). https://doi.org/10.1080/00036818808839825
3. Kilbas A A, Srivastava H M, Trujillo, j j: Theory and applications of fractional differential equations. North-Holland Mathematics Studies. 204, 7-10(2006).
4. Liu. L, Zhang. X, Jiang. J, Wu. Y : The unique solution of a class of sum mixed monotone operator equations and its application to fractional boundary value problems J. Nonlinear Sci. Appl. 9 (2016), 2943-2958. https://doi.org/10.22436/jnsa.009.05.87
5. Podlubny I: Fractional Differential Equations. Academic Press, San Diego, (1999).
6. Sang, Y: Existence and uniqueness of fixed points for mixed monotone operators with perturbations, Electronic Journal of Differential Equations, 233(2013)1-16.
7. Sang, Y: A class of Ï•-concave operators and applications, Fixed Point Theory and Applications, vol. 2013, 2013. https://doi.org/10.1186/1687-1812-2013-274
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Published
2021-12-18
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