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.
Citation: Anil Kumar, Muslim Malik, Mohammad Sajid, Dumitru Baleanu. Existence of local and global solutions to fractional order fuzzy delay differential equation with non-instantaneous impulses[J]. AIMS Mathematics, 2022, 7(2): 2348-2369. doi: 10.3934/math.2022133
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.
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