Nonlocal problems of fractional systems involving left and right fractional derivatives at resonance

Xiping Liu; Mei Jia; Zhanbing Bai; Xiping Liu; Mei Jia; Zhanbing Bai

doi:10.3934/math.2020214

AIMS Mathematics

2020, Volume 5, Issue 4: 3331-3345. doi: 10.3934/math.2020214

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Research article

Nonlocal problems of fractional systems involving left and right fractional derivatives at resonance

1.
College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
2.
College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao 266590, China

Received: 04 December 2019 Accepted: 28 February 2020 Published: 30 March 2020
MSC : 26A33, 34A08, 34B10, 65L10

In this paper, we study a class of nonlocal boundary value problems of fractional systems which involves left and right fractional derivatives at resonance. By using the coincidence degree theory, the solvability results for the problems are obtained under the resonant conditions. As an application of our results, we also deal with the existence result for the solution of fractional differential equation which involves both left and right fractional derivatives and satisfies certain boundary conditions under the resonant conditions. Finally, some examples are presented to illustrate our main results.
- fractional system,
- left and right fractional derivative,
- nonlocal problem,
- resonance condition
Citation: Xiping Liu, Mei Jia, Zhanbing Bai. Nonlocal problems of fractional systems involving left and right fractional derivatives at resonance[J]. AIMS Mathematics, 2020, 5(4): 3331-3345. doi: 10.3934/math.2020214

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Abstract

In this paper, we study a class of nonlocal boundary value problems of fractional systems which involves left and right fractional derivatives at resonance. By using the coincidence degree theory, the solvability results for the problems are obtained under the resonant conditions. As an application of our results, we also deal with the existence result for the solution of fractional differential equation which involves both left and right fractional derivatives and satisfies certain boundary conditions under the resonant conditions. Finally, some examples are presented to illustrate our main results.

References

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