The Existence and Uniqueness of the Solution of Difference Equation in Neutrosophic Environment via Generalized Hukuhara Difference Ideology

In real-world scenarios, the neutrosophic set or neutrosophic numbers have been widely used to deal with the uncertain difference equations of the corresponding uncertain discrete dynamical system. A situation where discrete changes occur with vague information of a neutrosophic sense can be dealt with by the neutrosophic difference equation. In this paper, a new metric is defined for the neutrosophic set, and the sense of generalized Hukuhara difference for the fuzzy numbers is extended to the neutrosophic numbers. The generalized Hukuhara difference of the type-I and type-II and their corresponding neutrosophic parametric representation are discussed. The existence and uniqueness conditions to obtain a solution of the difference equation in a neutrosophic environment are argued by some theorems. The theoretical concept has been applied to the logistic difference equation in a neutrosophic environment. We have applied both the type-I and type-II Hukuhara differences to the two different generalized Hukuhara difference forms of the logistic difference equation. The equilibrium points and their corresponding stability criteria are established to perceive the effect of the Hukuhara differences. Finally, the numerical examples and their graphical portrayal are provided to recognize the intuition of the introduced theory in this paper.