An estimation of effects of memory and learning experience on the eoq model with price dependent demand

In this article, an economic order quantity model has been studied in view of joint impacts of the memory and learning due to experiences on the decision-making process where demand is considered as price dependant function. The senses of memory and experience-based learning are accounted by the fractional calculus and dense fuzzy lock set respectively. Here, the physical scenario is mathematically captured and presented in terms of fuzzy fractional differential equation. The α-cut defuzzification technique is used for dealing with the crisp representative of the objective function. The main credit of this article is the introduction of a smart decision-making technique incorporating some advanced components like memory, self-learning and scopes for alternative decisions to be accessed simultaneously. Besides the dynamics of the EOQ model under uncertainty is described in terms of fuzzy fractional differential equation which directs toward a novel approach for dealing with the lot-sizing problem. From the comparison of the numerical results of different scenarios (as particular cases of the proposed model), it is perceived that strong memory and learning experiences with appropriate keys in the hand of the decision maker can boost up the profitability of the retailing process.

Existence, Uniqueness, and Eq–Ulam-Type Stability of Fuzzy Fractional Differential Equation

This paper concerns with the existence and uniqueness of the Cauchy problem for a system of fuzzy fractional differential equation with Caputo derivative of order q∈(1,2], 0cD0+qu(t)=λu(t)⊕f(t,u(t))⊕B(t)C(t),t∈[0,T] with initial conditions u(0)=u0,u′(0)=u1. Moreover, by using direct analytic methods, the Eq–Ulam-type results are also presented. In addition, several examples are given which show the applicability of fuzzy fractional differential equations.

Fuzzy Conformable Fractional Differential Equations

In this study, fuzzy conformable fractional differential equations are investigated. We study conformable fractional differentiability, and we define fractional integrability properties of such functions and give an existence and uniqueness theorem for a solution to a fuzzy fractional differential equation by using the concept of conformable differentiability. This concept is based on the enlargement of the class of differentiable fuzzy mappings; for this, we consider the lateral Hukuhara derivatives of order q ∈ 0,1 .

Invariant solutions of hyperbolic fuzzy fractional differential equations

We consider the hyperbolic type fuzzy fractional differential equation and derive the second-order fuzzy fractional differential equation using scaling transformation. We present a theoretical and a numerical method to find the invariant solutions of such equations. Also, we prove the existence and uniqueness results using Banach fixed point theorem. Numerical solutions are approximated using finite difference method. Finally, numerical examples are given to illustrate the obtained results.

On the Existence and Uniqueness for High Order Fuzzy Fractional Differential Equations with Uncertainty

A class fuzzy fractional differential equation (FFDE) involving Riemann-LiouvilleH-differentiability of arbitrary orderq>1is considered. Using Krasnoselskii-Krein type conditions, Kooi type conditions, and Rogers conditions we establish the uniqueness and existence of the solution after determining the equivalent integral form of the solution.