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Existence, uniqueness and matrix-valued fuzzy Mittag–Leffler–Hypergeometric–Wright stability for \(\mathfrak {P}\)-Hilfer fractional differential equations in matrix-valued fuzzy Banach space

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Abstract

We introduce a new class of fuzzy control functions and define the concept of matrix-valued fuzzy Mittag–Leffler–Hypergeometric–Wright stability. Then, we apply Radu–Mihet method derived from an alternative fixed point theorem to investigate existence, uniqueness and matrix-valued fuzzy Mittag–Leffler–Hypergeometric–Wright stability of a a class of \(\mathfrak {P}\)-Hilfer fractional differential equations in matrix-valued fuzzy Banach space. Next, we show the main results for unbounded domains. An example is given to illustrate the Mittag–Leffler–Hypergeometric–Wright stability for a fractional system.

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Acknowledgements

The authors are thankful to the area editor and referees for giving valuable comments and suggestions.

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Authors and Affiliations

  1. School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran

    Safoura Rezaei Aderyani & Reza Saadati

  2. Faculty of Engineering and Natural Sciences, Istinye University, Istanbul, Turkey

    Tofigh Allahviranloo

Authors
  1. Safoura Rezaei Aderyani
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  2. Reza Saadati
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  3. Tofigh Allahviranloo
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All authors conceived of the study, participated in its design and coordination, drafted the manuscript, participated in the sequence alignment, and read and approved the final manuscript.

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Correspondence to Reza Saadati or Tofigh Allahviranloo.

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Communicated by Marcos Eduardo Valle.

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Aderyani, S.R., Saadati, R. & Allahviranloo, T. Existence, uniqueness and matrix-valued fuzzy Mittag–Leffler–Hypergeometric–Wright stability for \(\mathfrak {P}\)-Hilfer fractional differential equations in matrix-valued fuzzy Banach space. Comp. Appl. Math. 41, 234 (2022). https://doi.org/10.1007/s40314-022-01935-x

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  • DOI: https://doi.org/10.1007/s40314-022-01935-x

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