Existence of Solutions for Anti-Periodic Fractional Differential Inclusions Involving ? -Riesz-Caputo Fractional Derivative

Dandan Yang and Chuanzhi Bai
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Dandan Yang: School of Mathematical Science, Huaiyin Normal University, Huaian 223300, Jiangsu, China
Chuanzhi Bai: School of Mathematical Science, Huaiyin Normal University, Huaian 223300, Jiangsu, China

Mathematics, 2019, vol. 7, issue 7, 1-15

Abstract: In this paper, we investigate the existence of solutions for a class of anti-periodic fractional differential inclusions with ψ -Riesz-Caputo fractional derivative. A new definition of ψ -Riesz-Caputo fractional derivative of order α is proposed. By means of Contractive map theorem and nonlinear alternative for Kakutani maps, sufficient conditions for the existence of solutions to the fractional differential inclusions are given. We present two examples to illustrate our main results.

Keywords: fractional differential inclusions; ? -Riesz-Caputo derivative; existence of solutions; fixed point theorem; anti-periodic boundary value problems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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