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Piecewise conformable fractional impulsive differential system with delay: existence, uniqueness and Ulam stability

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Abstract

Ideally, the state variable follows a constant motion law over time. However, due to the finiteness of motion speed, almost all systems have time delay. In this paper, we investigate a new class of piecewise conformable fractional impulsive differential system with delay under two point inhomogeneous boundary condition. In the system, the motion laws of state variable vary at different time periods, and they interact with each other through time delay “\(\tau \)” and time leading “\(-\tau \)”, so as to be more realistic. By employing the well-know fixed point theorems, the sufficient conditions for the existence and uniqueness of solutions to the system are established. Under the conditions of ensuring the existence of the system’s solutions, we conclude further that the system has Ulam–Hyers stability and Ulam–Hyers–Rassias stability by means of nonlinear functional analysis method. Finally, we give a feasible example to explain our result.

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Acknowledgements

This research was supported by National Natural Science Foundation of China (Grant No. 12371308). The authors would like to thank the anonymous reviewers and the editor for their constructive suggestions on improving the presentation of the paper.

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  1. Zhensheng Yu is contributed equally to this work.

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  1. College of Science, University of Shanghai for Science and Technology, 516 Jun Gong Rd., Shanghai, 200093, People’s Republic of China

    Luchao Zhang, Xiping Liu, Mei Jia & Zhensheng Yu

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  1. Luchao Zhang
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Zhang, L., Liu, X., Jia, M. et al. Piecewise conformable fractional impulsive differential system with delay: existence, uniqueness and Ulam stability. J. Appl. Math. Comput. 70, 1543–1570 (2024). https://doi.org/10.1007/s12190-024-02017-3

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