Shooting method for fuzzy two-point boundary value problems

Bede, Barnabás; Rudas, Imre J.

doi:10.1109/nafips.2012.6290986

Cited by 3 publications

(1 citation statement)

References 16 publications

(11 reference statements)

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“…Runge-Kutta method [156], Taylor method [157], Nystrom method [158], artificial neural network [159], and F-transform [160] have been proposed for solving FDEs under the concept of H-differentiability; and under Seikkaladifferentiability, the Runge-Kutta method has been presented in [161]. There have been many papers dedicated to finding solutions of FDEs under the concept of SGH-derivative among which are Runge-Kutta method [162], [163], reproducing kernel theory [164], extended Runge-Kutta [165], Euler method [166], differential transform method [167], fuzzy Sumudu transforms [168], [169], diameter-based method of a fuzzy function [170], fuzzy Fourier transform [171], Picard method [172], Laplace transform [173], [174], quasi-levelwise-system [175], and shooting method [176]. In addition, the variation of constant formula for a linear first order fuzzy differential equation with crisp coefficients and fuzzy initial condition has been introduced in [177], [178].…”

Section: Solution Methods Of Fdesmentioning

confidence: 99%

A Review on Fuzzy Differential Equations

Mazandarani

Xiu

2021

IEEE Access

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Since the term "Fuzzy differential equations" (FDEs) emerged in the literature in 1978, prevailing research effort has been dedicated not only to the development of the concepts concerning the topic, but also to its potential applications. This paper presents a chronological survey on fuzzy differential equations of integer and fractional orders. Attention is concentrated on the FDEs in which a definition of fuzzy derivative of a fuzzy number-valued function has been taken into account. The chronological rationale behind considering FDEs under each concept of fuzzy derivative is highlighted. The pros and cons of each approach dealing with FDEs are also discussed. Moreover, some of the proposed FDEs applications and methods for solving them are investigated. Finally, some of the future perspectives and challenges of fuzzy differential equations are discussed based on our personal view point.

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