Existence of solutions to fractional differential equations with multi-point boundary conditions at resonance in Hilbert spaces
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Date
2016-02-29
Authors
Zhou, Hua-Cheng
Ge, Fu-Dong
Kou, Chun-Hai
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
This article is devoted to investigating the existence of solutions to fractional multi-point boundary-value problems at resonance in a Hilbert space. More precisely, the dimension of the kernel of the fractional differential operator with the boundary conditions be any positive integer. We point out that the problem is new even when the system under consideration is reduced to a second-order ordinary differential system with resonant boundary conditions. We show that the considered system admits at least a solution by applying coincidence degree theory first introduced by Mawhin. An example is presented to illustrate our results.
Description
Keywords
Fractional differential equations, Resonance, Coincidence degree
Citation
Zhou, H. C., Ge, F. D., & Kou, C. H. (2016). Existence of solutions to fractional differential equations with multi-point boundary conditions at resonance in Hilbert spaces. Electronic Journal of Differential Equations, 2016(61), pp. 1-16.
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Attribution 4.0 International
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This work is licensed under a Creative Commons Attribution 4.0 International License.