In this research an analytic method is used to solve fuzzy heat equation with fuzzy initial values, which is based on Generalized Hukuhara differentiability. At first, we define fuzzy laplace transform in t considering x as a parameter on fuzzy functions u(x,t) and their derivatives by using Generalized Hukuhara differentiability. The fuzzy laplace transform is used in an analytic method for solving the fuzzy partial differential equation with Generalized Hukuhara differantiation. Finally, the method is explained by presenting examples.

An analytical fuzzy solution is achieved by means of the fuzzy d’, Alembert formula for the fuzzy one-dimensional homogeneous wave equation in a half-line considering the Generalized Hukuhara partial differentiability of the solution. In the current article, the exclusive solution and the stability of the homogeneous fuzzy wave equations are brought into existence. Eventually, given the various instances represented, the efficacy and accuracy of the method are scrutinized.

In this study, an economic production quantity (EPQ) model with deterioration is developed where the production rate is stock dependent and the demand rate is unit selling price and stock dependent. The low unit selling price and more stocks correspond high demand but more stock corresponds to slow production because of the avoidance of unnecessary stocks. First of all, we develop the production model by solving some ordinary differential equations having deterministic profit function under some specific assumptions. Later, we develop the fuzzy model by solving the fuzzy differential equations using Generalized Hukuhara derivative. In fact, the differential equation of the model has been split into two parts namely gH(L-R) and gH(R-L) on the basis of left(L) and right(R) α- cuts of fuzzy numbers for which the problem itself is transformed into multi-objective EPQ problem. A new formula of aggregation of several objective values obtained at different aspiration levels has been discussed to defuzzify the fuzzy multi-objective problems. We solve the crisp and fuzzy models using LINGO software. Numerical and graphical illustrations confirm that the model under Generalized Hukuhara derivative of (R-L) type contributes more profit which is one of the basic novelties of the proposed approach.

In this present study, the tumor growth model using the Gompertz equation with the Allee effect is developed under a fuzzy environment using the Generalized Hukuhara Derivative  (GHD) approach. To capture the tumor growth patterns with the Allee threshold, the parameters present in the model vary from time to time, and in real life, it is very difficult to estimate the exact cell count. In this vague situation, the initial condition, coefficient, and both together are taken as the fuzzy number. In this paper, the  GHD  approach is used to solve the fuzzy tumor growth model in which four different cases are considered with respect to (i)-gH differentiability and (ii)-gH differentiability concept. The main objective of this study is to present a significant reduction in uncertainty while modeling the tumor growth in a fuzzy environment with the Allee effect. Finally, the proposed model and technique are illustrated by numerical simulation and analysis of tumor growth is conducted.

This paper introduces a novel approach to obtaining analytical solutions forfuzzy fractional differential equations in the context of weighted Caputo-type GeneralizedHukuhara derivatives. The paper proposes the use of non-singular kernels to improve theaccuracy of fractional calculus in fuzzy space and establishes the uniqueness of solutions forfuzzy fractional differential equations. The paper also introduces the concept of fuzzy Laplacetransforms to facilitate the solution of these equations. Practical examples, such as the fuzzyfractional Newton’s law of heating and cooling, are provided to demonstrate the effectivenessof the proposed method. Overall, this paper contributes to the development of practical solutionsfor real-world problems in fuzzy space and enhances the accuracy of fractional calculusin this context.

In this paper, we introduce a new method for solving fuzzy Bernoulli differential equation (FBDE) under Generalized differentiability. At the beginning, by stating the theorems, we define nth power of LR fuzzy function and the derivative of LR fuzzy function. Then, we obtain core function to determine LR fuzzy solution, through solving 1-cut FBDE, and calculate spread functions by finding the sign of real valued functions of coefficients of FBDE and finding the sign of core function. Also, numerical examples are presented to verify the effectiveness of the proposed method.

In the present paper, the analytical solution for an exact second order fuzzy initial value problem under Generalized Hukuhara differentiability is obtained. First the solution of first order linear fuzzy differential equation under Generalized Hukuhara differentiability is investigated using integration factor methods in two cases. The second based on the type of Generalized Hukuhara differentiability, the analytical solution of an exact second order fuzzy initial value problem is derived in two senses of differentiability. Also, several properties for Generalized Hukuhara differentiability are obtained on the topics, such as, the univariate fuzzy chain rules, fuzzy integration by parts, among others. At the end, some illustrative examples are presented and these examples show the behavior of the ‎solutions.