Fuzzy Fractional Quadratic Regulator Problem Under Granular Fuzzy Fractional Derivatives

Najariyan, Marzieh; Zhao, Yi

doi:10.1109/tfuzz.2017.2783895

Cited by 63 publications

(16 citation statements)

References 37 publications

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“…At the same time, by combining Riemann-Liouville and Caputo's derivatives with gr-derivative, i.e. granular Riemann-Liouville derivative and granular Caputo derivative, granular fuzzy fractional derivatives emerged in [94]. Granular fuzzy fractional integral has also been presented in this work.…”

Section: B Fractional Order Fuzzy Differential Equationsmentioning

confidence: 94%

“…Under the concept of Caputo-type H 2 -derivative, approximate solutions of type-2 fuzzy fractional differential equations have been obtained using the predictor-evaluatecorrector-evaluate (PECE) method in [126]. By presenting an approximation of the granular fuzzy fractional integral and the granular Caputo fuzzy fractional derivative, an approximate solution for FFDEs under the concept of gr-Caputo fuzzy fractional derivative has been given in [94]. Finally, FFDEs under the concept of conformable SGH-derivative have been solved by the aid of Taylor series expansion in [150] and reproducing kernel Hilbert space method in [151].…”

Section: Solution Methods Of Fdesmentioning

confidence: 99%

“…The performance criteria of second-order fuzzy linear dynamical systems and fuzzy tracking control of fuzzy linear dynamical systems under the concept of gr-differentiability have been investigated, respectively, in [95], [101]. By the aid of gr-Caputo derivative concept, the fuzzy fractional quadratic regulator problem was studied in [94] where a fuzzy feedback control was designed. For further study about the applications of FDEs of fractional order in optimal control and controllability refer to [191].…”

Section: Applications Of Fdesmentioning

confidence: 99%

See 2 more Smart Citations

A Review on Fuzzy Differential Equations

Mazandarani¹,

Li²

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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Section: B Fractional Order Fuzzy Differential Equationsmentioning

confidence: 94%

Section: Solution Methods Of Fdesmentioning

confidence: 99%

Section: Applications Of Fdesmentioning

confidence: 99%

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A Review on Fuzzy Differential Equations

Mazandarani¹,

Li²

2021

IEEE Access

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“…studied some optimal control problems of fuzzy linear dynamical systems (Mazandarani and Zhao 2018; Mazandarani and Pariz 2018) by using gr-derivatives. Najariyan and Zhao (2018) developed new definitions of redgranular fractional derivatives, granular fractional integrals, to study the approximation solution of fuzzy fractional quadratic regulator problems.…”

Section: Second Approach Based On Generalized Hukuhara Differentiabilmentioning

confidence: 99%

Fuzzy delay differential equations under granular differentiability with applications

Son¹,

Long

Dong

2019

Comp. Appl. Math.

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In this paper, we consider a new setting of fuzzy delay differential equations by employing the concepts of granular differentiability. Firstly, we establish some basic properties of complete granular metric space. Then we study the local and global existence and uniqueness of integral fuzzy solution. For the first task, we use successive approximation technique combined with Gronwall's lemma. The second task will be solved by Banach contraction principle in weighted metric space defined by granular distance. Additionally, we demonstrate the theoretical results by solving some real-world models in both analytical method and numerical method. The first model is often referred to the exponential growth, namely time-delay growth Malthusian model. The second model is one type of dynamical systems, which is used for studies involving large amounts of tissues, called Ehrlich ascites tumor model with delay. Furthermore, we introduce the Mackey-Glass model which is considered as a useful tool for times series prediction in the neutral network and fuzzy logic fields. Finally, we represent the surface of fuzzy solution for visible identification mark-on. Keywords Granular differentiability • Fuzzy delay differential equations • Malthusian growth model • Ehrlich ascites tumor model • Mackey-Glass time series model Mathematics Subject Classification 34A07 • 35R13 Communicated by Anibal Tavares de Azevedo.

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“…The chaotic behaviour of love affairs model of fractional‐order system with fuzzy membership function as an external force was obtained by Huang and Bae [32]. In [33], a class of uncertain linear dynamical systems called fuzzy fractional linear dynamical systems were investigated and obtain the optimal control inputs of fuzzy fractional quadratic regulator problem under Granular fuzzy fractional derivatives.…”

Section: Introductionmentioning

confidence: 99%

Analysis for fractional‐order predator–prey model with uncertainty

Narayanamoorthy¹,

Băleanu²,

Thangapandi³

et al. 2019

IET Systems Biology

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Here, the authors analyse the fractional-order predator-prey model with uncertainty, due to the vast applications in various ecological systems. The most of the ecological model do not have exact analytic solution, so they proposed a numerical technique for an approximate solution. In the proposed method, they have implemented the higher order term into the fractional Euler method to enhance the precise solution. Further, the present attempt is aimed to discuss the solutions of the FPPM with uncertainty (fuzzy) initial conditions. The initial conditions of the predator-prey model were taken as fuzzy initial conditions due to the fact that the ecological model highly depends on uncertain parameters such as growth/decay rate, climatic conditions, and chemical reactions. Finally, the numerical example manifest that the proposed method is authentic, applicable, easy to use from a computational viewpoint and the acquired outcomes are balanced with the existing method (HPM), which shows the efficiency of the proposed method.

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Fuzzy Fractional Quadratic Regulator Problem Under Granular Fuzzy Fractional Derivatives

Cited by 63 publications

References 37 publications

A Review on Fuzzy Differential Equations

A Review on Fuzzy Differential Equations

Fuzzy delay differential equations under granular differentiability with applications

Analysis for fractional‐order predator–prey model with uncertainty

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