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| Unique Solution for a General Coupled System of Fractional Differential Equations |
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| KeyWord:Existence and uniqueness, coupled system of fractional differential equations, fixed point theorem, $\varphi$-$(h,e)$-concave operators |
| Author Name | Affiliation | | Mengjiao Zhao | School of Mathematical Sciences, Shanxi University, Taiyuan 030006, Shanxi, China | | Chengbo Zhai | School of Mathematical Sciences, Shanxi University, Taiyuan 030006, Shanxi, China
Key Laboratory of Complex Systems and Data Science of Ministry of Education, Shanxi University, Taiyuan 030006, Shanxi, China |
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| Abstract: |
| This paper discusses a new coupled system of Riemann-Liouville fractional differential equations, in which the nonlinear terms include the Riemann-Liouville fractional integrals and the boundary value problems involve three-points. We seek also for the existence and uniqueness of solutions for this new system. We first get some useful properties of the Green's function generated by the system, and then we apply a fixed point theorem of increasing $\varphi$-$(h,e)$-concave operators to this new coupled system. Finally, we gain the existence and uniqueness results of the solution for this problem. In the end, a concrete example is structured to illustrate the main result. |
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