Fuzzy Differential Equations and Applications for Engineers and Scientists

Chakraverty, Snehashish; Tapaswini, Smita; Behera, Diptiranjan

doi:10.1201/9781315372853

Cited by 58 publications

(30 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Moreover, some of the other proposed applications of FDEs can be found in [200] for a predatorprey model, in [201] for production inventory model, in [72] for an economical investment, and in [202] for oil palm frond. For further applications of FDEs refer to [203]- [205].…”

Section: Applications Of Fdesmentioning

confidence: 99%

A Review on Fuzzy Differential Equations

Mazandarani¹,

Li²

2021

IEEE Access

View full text Add to dashboard Cite

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.

show abstract

Section: Applications Of Fdesmentioning

confidence: 99%

A Review on Fuzzy Differential Equations

Mazandarani¹,

Li²

2021

IEEE Access

View full text Add to dashboard Cite

show abstract

“…In this segment, some basic definitions, and notations of fuzzy variables are discussed (see References [25][26][27]).…”

Section: Preliminariesmentioning

confidence: 99%

“…Kaleva [23] and Seikkala [24] studied the fuzzy differential equations (FDEs) and initial value problems. Various problems related to the differential FDEs are broadly studied by Chakraverty et al (see References [25][26][27]). As fuzzy fractional differential equations (FFDEs) are quite challenging to solve as compared to fractional differential equations, computationally efficient numerical methods should be developed.…”

Section: Introductionmentioning

confidence: 99%

On the Solution of an Imprecisely Defined Nonlinear Time-Fractional Dynamical Model of Marriage

2019

View full text Add to dashboard Cite

The present paper investigates the numerical solution of an imprecisely defined nonlinear coupled time-fractional dynamical model of marriage (FDMM). Uncertainties are assumed to exist in the dynamical system parameters, as well as in the initial conditions that are formulated by triangular normalized fuzzy sets. The corresponding fractional dynamical system has first been converted to an interval-based fuzzy nonlinear coupled system with the help of a single-parametric gamma-cut form. Further, the double-parametric form (DPF) of fuzzy numbers has been used to handle the uncertainty. The fractional reduced differential transform method (FRDTM) has been applied to this transformed DPF system for obtaining the approximate solution of the FDMM. Validation of this method was ensured by comparing it with other methods taking the gamma-cut as being equal to one.

show abstract

“…First-order linear fuzzy differential equations have inspired several authors to focus on solving them numerically since they appear in many real-world applications. ese applications include different fields of science such as medical diagnosis, biology, and civil engineering and also in the field of economics [11] where the information are not given in the crisp set [12]. Based on Zadeh's extension principle, a new fuzzy version of Euler's method was developed by Ahamed and Hasan [13].…”

Section: Introductionmentioning

confidence: 99%

A Novel Approach for Solving Fuzzy Differential Equations Using Cubic Spline Method

Karpagappriya

Alessa

Jayaraman

et al. 2021

Mathematical Problems in Engineering

View full text Add to dashboard Cite

Ambiguity in real-world problems can be modeled into fuzzy differential equations. The main objective of this work is to introduce a new class of cubic spline function approach to solve fuzzy initial value problems efficiently. Further, the convergence of this method is shown. As it is a single-step method that converges faster, the complexity of the proposed method is too low. Finally, a numerical example is illustrated in order to validate the effectiveness and feasibility of the proposed method, and the results are compared with the exact as well as Taylor’s method of order two.

show abstract

Fuzzy Differential Equations and Applications for Engineers and Scientists

Cited by 58 publications

References 0 publications

A Review on Fuzzy Differential Equations

A Review on Fuzzy Differential Equations

On the Solution of an Imprecisely Defined Nonlinear Time-Fractional Dynamical Model of Marriage

A Novel Approach for Solving Fuzzy Differential Equations Using Cubic Spline Method

Contact Info

Product

Resources

About