A comparison between numerical methods for solving Fuzzy fractional differential equations

Abstract

In this paper, numerical simulation of linear and nonlinear fuzzy initial value problems of fractional order has been done. A modi cation in the improved Euler's method for fuzzy fractional order is proposed and utilized. Also, the two component homotopy perturbation method also known as a modi ed homotopy perturbation method (MHPM) is employed to solve the considered problems. The results obtained from the considered techniques are compared. These methods are illustrated by solving several examples. E ciency and exactness of results worked out from MHPM is examined from the tables and comparatively it is found that MHPM is more accurate and closer to the exact solutions than the existing methods.

On the solution of fuzzy differential equations by Fuzzy Sumudu Transform

“…Fuzzy theory plays an important role in modeling dynamical systems under uncertainty. Fuzzy linear di erential equations are one of the simplest fuzzy di erential models which have signi cant importance in many applications [18][19][20][21][22][23][24][25][26]. Here fuzzy di erential equations are considered under generalized Hukuhara di erentiability.…”

A Single Layer Functional Link Artificial Neural Network based on Chebyshev Polynomials for Neural Evaluations of Nonlinear Nth Order Fuzzy Differential Equations

“…This section contains brief description about fuzzy set theory and differentiability of fuzzy-valued functions that are considerably important for the remaining paper. The detailed definitions and properties of fuzzy set theory are greatly found in [1]- [14].…”

“…As a result, the intricacy of integrations, which exist in other methods in case of nonlinear functions [14], become extinct. Let the considered nonlinear FDE be of the form…”

“…In recent times, many ways and means are being established to analyze and simulate fuzzy differential equations. For instance, Euler type methods [4], shooting method [5], fuzzy Picard method [6], fuzzy Laplace transform [7], fuzzy Sumudu transform [8], Runge-Kutta method [9]- [10], fuzzy variational iteration method [11], Adams predictor corrector [12], Taylor method [13], modified Homotopy perturbation method [14], to name a few. Along with these techniques, various papers are found where the latest methods, like different artificial neural networks [15]- [16], are also carried out for the evaluation of FDEs.…”

A Neural Computational Intelligence Method Based on Legendre Polynomials for Fuzzy Fractional Order Differential Equation

“…It is to be noted that the new trail points array will be in the same domain, as was in the training procedure, and should be equally spaced. [18]. Table 3 …”