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Issue:Solvability of an intuitionistic fuzzy fractional differential equation of second type

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Title of paper: Solvability of an intuitionistic fuzzy fractional differential equation of second type
Author(s):
Hamid Sadiki
Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, Beni Mellal, Morocco
h.sadiki@usms.ma
Khadija Oufkir
Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, Beni Mellal, Morocco
oufkirkhadijabzou@gmail.com
Aziz El Ghazouani
Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, Beni Mellal, Morocco
aziz.elghazouani@usms.ma
M'hamed Elomari
Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, Beni Mellal, Morocco
m.elomari@usms.ma
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 30 (2024), Number 4, pages 349–367
DOI: https://doi.org/10.7546/nifs.2024.30.4.349-367
Download:  PDF (302  Kb, File info)
Abstract: In this research, we provide certain novel requirements for the existence and uniqueness of fuzzy solutions for a type of non-linear intuitionistic fuzzy fractional equations with intuitionistic fuzzy initial conditions under the intuitionistic fuzzy fractional derivative of order [math]\displaystyle{ n \in (0,3) }[/math] in Caputo sense. The required findings are demonstrated by employing the Banach fixed point theorem, the intuitionistic fuzzy Laplace transform and the Mittag-Leffler function. An example is provided to demonstrate the reliability of our findings.
Keywords: Intuitionistic fuzzy set of second type, Intuitionistic fuzzy number, Intuitionistic fuzzy fractional derivative of Caputo sense, Intuitionistic fuzzy Laplace transform, Banach fixed point theorem, Mittag-Leffler function.
AMS Classification: 26A33, 34A07, 34K37.
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