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Research Article | Open Access

Existence of local and global solutions to fractional order fuzzy delay differential equation with non-instantaneous impulses

Anil Kumar1, Muslim Malik1, Mohammad Sajid2( ), Dumitru Baleanu3,4
School of Basic Sciences, Indian Institute of Technology Mandi, India
Department of Mechanical Engineering, College of Engineering, Qassim University, Buraidah-51452, Al Qassim, Saudi Arabia
Cankaya University, Department of Mathematics and Computer Sciences, Ankara, Turkey
Institute of Space Sciences, Magurele-Bucharest, Romania
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Abstract

The main concern of this manuscript is to examine some sufficient conditions under which the fractional order fuzzy delay differential system with the non-instantaneous impulsive condition has a unique solution. We also study the existence of a global solution for the considered system. Fuzzy set theory, Banach fixed point theorem and Non-linear functional analysis are the major tools to demonstrate our results. In last, an example is given to illustrate these analytical results.

Keywords

fuzzy delay differential equationsAtangana-Baleanu fractional derivativefixed point theoremnon-instantaneous impulses
CLC number: 03B52, 34A07, 34A08, 34A37

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AIMS Mathematics
Volume 7 Issue 2,
February 2022
Pages 2348-2369
DOI: 10.3934/math.2022133

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Cite this article:
Kumar A, Malik M, Sajid M, et al. Existence of local and global solutions to fractional order fuzzy delay differential equation with non-instantaneous impulses. AIMS Mathematics, 2022, 7(2): 2348-2369. https://doi.org/10.3934/math.2022133

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Received: 09 September 2021
Accepted: 01 November 2021
Published: 15 February 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)