Solution of Fuzzy Differential Equations using new Modified Fuzzy Sumudu Transform and its Applications

Abstract

Fuzzy differential equation plays a very important role in solving uncertainty problems in engineering and real life. The behaviors of the Dengue Virus Infected Population model in Fuzzy and Interval Environment are also discussed here. Modeling the environments in the fuzzy differential equation and used to solve in different environments to strong solution by triangular fuzzy numbers. To identify these two different environments, how the behaviors of the model can change with two examples in each environment. This proposes a method for solving various types of fuzzy linear Volterra Integro- Differential equation considering the initial condition as a generalized triangular fuzzy number. The proposed method is based on the Fuzzy Sumudu transform (FST). Some results based on the properties of FST are also proposed. The introduction of a new way to solve an ordinary differential equation by using Nonagonal intuitionistic fuzzy numbers. A new version of INFN addressed here and formed different types of NIFN System with properties of said fuzzy numbers. Demonstration of a Nonagonal intuitionistic fuzzy solution in FDE is carried out with INFN.Any real-life problems can be modeled by a differential equation. In this second- order fuzzy differential equation is converted to fuzzy differential equations and solved by fuzzy Sumudu transforms method with initial values as intuitionistic triangular fuzzy numbers. To understand the proposed method and solved a numerical problem with graphical representations. To find a solution for an RL electric circuit problem by fuzzy Sumudu transform method. The solution method of the differential equation is also described by fuzzy Sumudu transform with the initial condition as intuitionistic triangular fuzzy numbers. It is discussed in different cases; fuzzy numbers are taken for initial condition as generalized intuitionistic fuzzy numbers (GNFNs).