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Necessary and sufficient condition for the existence of solutions to two-point boundary value problem of fuzzy linear multi-term fractional differential equations

  • Fuzzy systems and their mathematics
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Abstract

To solve problems such as nonexistence of solutions to two-point boundary value problem of fuzzy linear multi-term fractional differential equations with variable coefficients, it is important to consider the necessary and sufficient condition for the existence of solutions. Choe et al. (Abstr Appl Anal 5129013:1–18, 2019) only obtained the sufficient condition for the existence of solutions. In this paper, we study a necessary and sufficient condition and then derive the solution expression of the proposed problem with constant coefficients. First, we obtain the cut problem with inequality constraints corresponding to the fuzzy two-point boundary value problem and present the necessary and sufficient condition for the fuzzy value function constructed from this cut problem to be the solution to the proposed problem. Also the solution expression is presented by using the multivariate Mittag–Leffler function. Some examples are given to illustrate our results.

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Acknowledgements

The author is very grateful to the referees for their valuable suggestions, which helped to improve the paper significantly.

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  1. Faculty of Mathematics, Kim Il Sung University, Pyongyang, Democratic People’s Republic of Korea

    Kinam Sin & Sunghyok Kwon

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  1. Kinam Sin
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  2. Sunghyok Kwon
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Correspondence to Kinam Sin.

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Sin, K., Kwon, S. Necessary and sufficient condition for the existence of solutions to two-point boundary value problem of fuzzy linear multi-term fractional differential equations. Soft Comput 27, 1401–1414 (2023). https://doi.org/10.1007/s00500-022-07639-y

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