A Review on Fuzzy Differential Equations

Mazandarani, Mehran; Li, Xiu

doi:10.1109/access.2021.3074245

Cited by 35 publications

(11 citation statements)

References 205 publications

(176 reference statements)

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“…The uncertainty in FDEs is considered as fuzzy numbers that are a sort of knowledge of experts. A considerable number of studies have been conducted on fuzzy differential equations among which the most important is a review on fuzzy differential equations that recently Mazandarani et al in [1] elegantly has elaborated on all the aspects of fuzzy differential equations. A large number of possible applications of FDEs has been cited in [1] among which we shall recall few of them as follows.…”

Section: Introductionmentioning

confidence: 99%

“…A considerable number of studies have been conducted on fuzzy differential equations among which the most important is a review on fuzzy differential equations that recently Mazandarani et al in [1] elegantly has elaborated on all the aspects of fuzzy differential equations. A large number of possible applications of FDEs has been cited in [1] among which we shall recall few of them as follows. Fuzzy delay differential equations under the concept of granular calculus has been studied in [2] .…”

Section: Introductionmentioning

confidence: 99%

“…However, in the mentioned papers and some other papers, concepts of fuzzy derivatives have been used which are based on FSIA approach and then they suffer from many shortcomings. In the sequel we explain briefly a few of the drawbacks that stem from these concepts, for more details see [1,19] .…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Tracking Control of a Class of Fuzzy Dynamical Systems under the Concept of Granular Differentiability

Abbasi¹,

Jalali²

2023

Fuzzy Information and Engineering

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In this work, the tracking control of a class of uncertain linear dynamical systems is investigated. The uncertainty is considered to be represented as fuzzy numbers, and hence, these uncertain dynamical systems are referred to as fuzzy linear dynamical systems, which are presented in the form of fuzzy differential equations (FDEs). The solution of an FDE is found using an approach called relative-distance-measure fuzzy interval arithmetic and under the granular differentiability concept. The control objective is to provide a control law such that the output of the system tracks a desired reference input in the presence of uncertainties. To this end, a theorem is proposed, which suggests that the control law should take the form of a feedback of fuzzy states with fuzzy gains and a fuzzy pre-compensator. However, since the fuzzy states of the system may not always be measurable, a fuzzy observer is designed for the estimation of such fuzzy states. It is also clearly shown that the generalized Hukuhara differentiability concept is unable for solving the problem examined in this study. Finally, the efficiency of the approach is examined for a plane landing control problem.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Tracking Control of a Class of Fuzzy Dynamical Systems under the Concept of Granular Differentiability

Abbasi¹,

Jalali²

2023

Fuzzy Information and Engineering

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“…On the contrary, fuzzy differential equations (FDEs) are a valuable tool to model a dynamic system that is ambiguous in its existence and comportments. Since the FDEs have been used widely to model scientific and engineering problems, they have become a popular topic among researchers [2]. There are many practical problems with the solution of FDEs that satisfy initial [3] or boundary [4] values conditions.…”

Section: Introductionmentioning

confidence: 99%

Efficient approximate analytical methods for nonlinear fuzzy boundary value problem

Jameel

Saleh

Azmi

et al. 2022

IJECE

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This paper aims to solve the nonlinear two-point fuzzy boundary value problem (TPFBVP) using approximate analytical methods. Most fuzzy boundary value problems cannot be solved exactly or analytically. Even if the analytical solutions exist, they may be challenging to evaluate. Therefore, approximate analytical methods may be necessary to consider the solution. Hence, there is a need to formulate new, efficient, more accurate techniques. This is the focus of this study: two approximate analytical methods-homotopy perturbation method (HPM) and the variational iteration method (VIM) is proposed. Fuzzy set theory properties are presented to formulate these methods from crisp domain to fuzzy domain to find approximate solutions of nonlinear TPFBVP. The presented algorithms can express the solution as a convergent series form. A numerical comparison of the mean errors is made between the HPM and VIM. The results show that these methods are reliable and robust. However, the comparison reveals that VIM convergence is quicker and offers a swifter approach over HPM. Hence, VIM is considered a more efficient approach for nonlinear TPFBVPs.

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“…Modeling like biological population models, the predator-prey models and infectious diseases models, etc are generalized to fractional order. Fractional calculus is not only a productive and emerging field, but it also represents a new philosophy, how to construct and apply a certain type of nonlocal operator to real-world problems [17,18,19,26,27,32,33].…”

Section: Introductionmentioning

confidence: 99%

Generalized Hukuhara conformable fractional derivative and its application to fuzzy fractional partial differential equations

et al. 2022

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The main focus of this paper is to develop an efficient analytical method to obtain the traveling wave fuzzy solution for the fuzzy generalized Hukuhara conformable fractional equations by considering the type of generalized Hukuhara conformable fractional differentiability of the solution. To achieve this, the fuzzy conformable fractional derivative based on the generalized Hukuhara differentiability is defined, and several properties are brought on the topic, such as switching points and the fuzzy chain rule. After that, a new analytical method is applied to find the exact solutions for two famous mathematical equations: the fuzzy fractional Wave equation and the fuzzy fractional Diffusion equation. The present work is the first report in which the fuzzy traveling wave method is used to design an analytical method to solve these fuzzy problems. The final examples are asserted that our new method is applicable and efficient.

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A Review on Fuzzy Differential Equations

Cited by 35 publications

References 205 publications

Tracking Control of a Class of Fuzzy Dynamical Systems under the Concept of Granular Differentiability

Tracking Control of a Class of Fuzzy Dynamical Systems under the Concept of Granular Differentiability

Efficient approximate analytical methods for nonlinear fuzzy boundary value problem

Generalized Hukuhara conformable fractional derivative and its application to fuzzy fractional partial differential equations

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