AIMS Mathematics, 2020, 5(4): 3331-3345. doi: 10.3934/math.2020214.

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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

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.
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Keywords 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. AIMS Mathematics, 2020, 5(4): 3331-3345. doi: 10.3934/math.2020214

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