Existence of solutions to fractional differential equations with multi-point boundary conditions at resonance in Hilbert spaces

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. <i>Electronic Journal of Differential Equations, 2016</i>(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.

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