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Qualitative Behaviour of a Caputo Fractional Differential System

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Abstract

In this article, we investigate a new system of fractional differential equations with integral boundary conditions. The proposed problem contains Caputo fractional derivative operators, integer derivatives and Riemann integral boundary values. We get the existence and uniqueness of solutions for the new system of fractional differential equations based on a fixed point theorem of increasing \(\phi \)-(h, e)-concave operators. The results show that the unique solution exists in a given set and can be approximated by making an iterative sequence for any initial point in the given set. Further, an example is given to illustrate the effectiveness and applicability of our main results.

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Authors and Affiliations

  1. School of Mathematical Sciences, Shanxi University, Taiyuan, 030006, Shanxi, People’s Republic of China

    Ruixiong Fan, Nan Yan & Chengbo Zhai

  2. Shanxi Vocational University of Engineering Science and Technology, Taiyuan, 030619, Shanxi, People’s Republic of China

    Chen Yang

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  1. Ruixiong Fan
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  2. Nan Yan
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The authors declare that the study was realized in collaboration with the same responsibility. Ruixiong Fan and Nan Yan wrote the main manuscript text . Chen Yang and Chengbo Zhai prepared Figures 1-2. All authors read and approved the final manuscript.

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Correspondence to Chengbo Zhai.

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Fan, R., Yan, N., Yang, C. et al. Qualitative Behaviour of a Caputo Fractional Differential System. Qual. Theory Dyn. Syst. 22, 143 (2023). https://doi.org/10.1007/s12346-023-00836-6

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