Generalized Hukuhara Weak Solutions for a Class of Coupled Systems of Fuzzy Fractional Order Partial Differential Equations without Lipschitz Conditions

Fan Zhang, Heng-You Lan () and Hai-Yang Xu
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Fan Zhang: College of Mathematics and Statistics, Sichuan University of Science & Engineering, Zigong 643000, China
Heng-You Lan: College of Mathematics and Statistics, Sichuan University of Science & Engineering, Zigong 643000, China
Hai-Yang Xu: College of Mathematics and Statistics, Sichuan University of Science & Engineering, Zigong 643000, China

Mathematics, 2022, vol. 10, issue 21, 1-21

Abstract: As is known to all, Lipschitz condition, which is very important to guarantee existence and uniqueness of solution for differential equations, is not frequently satisfied in real-world problems. In this paper, without the Lipschitz condition, we intend to explore a kind of novel coupled systems of fuzzy Caputo Generalized Hukuhara type (in short, gH -type) fractional partial differential equations. First and foremost, based on a series of notions of relative compactness in fuzzy number spaces, and using Schauder fixed point theorem in Banach semilinear spaces, it is naturally to prove existence of two classes of gH -weak solutions for the coupled systems of fuzzy fractional partial differential equations. We then give an example to illustrate our main conclusions vividly and intuitively. As applications, combining with the relevant definitions of fuzzy projection operators, and under some suitable conditions, existence results of two categories of gH -weak solutions for a class of fire-new fuzzy fractional partial differential coupled projection neural network systems are also proposed, which are different from those already published work. Finally, we present some work for future research.

Keywords: coupled system of fuzzy Caputo gH -type fractional partial differential equations; Schauder fixed point theorem; relative compactness in fuzzy number spaces; projection neural network; existence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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