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Applications of contractive-like mapping principles to fuzzy fractional integral equations with the kernel \(\psi \)-functions

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Abstract

In this work, we present a new class of generalized fractional integral equations with respect to the kernel \(\psi \)-function under the fuzzy concept. The results of this problem can be used to recover a wide class of fuzzy fractional integral equations by the choice of the kernel \(\psi \)-function. Without the Lipschitzian right-hand side, we investigate the existence and uniqueness of the fuzzy solutions by employing the fixed point theorem of weakly contractive mappings in the partially ordered space of fuzzy numbers. The proposed approach is based on the concept of a fuzzy metric space endowed with a partial order and the altering distance functions. In addition, the continuous dependence of solutions on the order and the initial condition of the given problem is also shown. Some concrete examples are presented in order to consolidate the obtained result.

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Acknowledgements

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

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Authors and Affiliations

  1. Institute of Research and Development, Duy Tan University, Danang, 550000, Vietnam

    Ho Vu

  2. Faculty of Natural Sciences, Duy Tan University, Danang, 550000, Vietnam

    Ho Vu

  3. Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Ngo Van Hoa

  4. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Ngo Van Hoa

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  1. Ho Vu
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  2. Ngo Van Hoa
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Correspondence to Ngo Van Hoa.

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Vu, H., Van Hoa, N. Applications of contractive-like mapping principles to fuzzy fractional integral equations with the kernel \(\psi \)-functions . Soft Comput 24, 18841–18855 (2020). https://doi.org/10.1007/s00500-020-05115-z

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