New Results on Multiple Solutions for Nth-Order Fuzzy Differential Equations under Generalized Differentiability

Abstract

We firstly present a generalized concept of higher-order differentiability for fuzzy functions. Then we interpret Nth-order fuzzy differential equations using this concept. We introduce new definitions of solution to fuzzy differential equations. Some examples are provided for which both the new solutions and the former ones to the fuzzy initial value problems are presented and compared. We present an example of a linear second-order fuzzy differential equation with initial conditions having four different solutions.

A boundary value problem for second order fuzzy differential equations

“…Now we recall some definitions and theorems for a first order derivative [12] and higher order derivatives based on the selection of derivative type in each step of differentiation [13].…”

“…Hence, the fuzzy solution behaves quite differently from the crisp solution. The strongly generalized differentiability was introduced in [10] and studied in [8,[11][12][13][14]. This concept allows us to resolve the above-mentioned shortcoming.…”

Approximate solution of second-order fuzzy boundary value problem

“…Recently, some mathematicians have become interested in finding the solutions to the fuzzy linear and nonlinear differential equation,and fuzzy integral equation [19,18,15,5,3,25,4,24,8]. The goal of this paper is to introduce an new approach by using generalized concepts [2,21,23,22,20,14,16,9,1] for the solution of second-order fuzzy boundary value problem…”

Nth-order Fuzzy Differential Equations Under Generalized Differentiability

“…al [19], investigated the multiple solution of Nth-order fuzzy differential equations under generalized differentiability. Also, Nieto et.…”