Concreted solutions to fuzzy linear fractional differential equations

Chehlabi, M.; Allahviranloo, Tofigh

doi:10.1016/j.asoc.2016.03.011

Cited by 39 publications

(6 citation statements)

References 25 publications

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“…The suggested algorithm for the FFDEs use the fuzzy fractional derivative of Caputo type in the range of α ∈ (0, 1] and is potentially useful in solving fractional viscoelastic problems under uncertainty. Chehlabi and Allahviranloo [27] studied fuzzy linear fractional differential equations of order 0 < α ≤ 1 under Riemann-Liouville H-differentiability. Also, it is corrected some previous results and obtained new solutions by using fractional hyperbolic functions and their properties.…”

Section: Introductionmentioning

confidence: 99%

A survey on fuzzy fractional differential and optimal control nonlocal evolution equations

Agarwal

Băleanu

Nieto

et al. 2018

Journal of Computational and Applied Mathematics

149

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We survey some representative results on fuzzy fractional differential equations, controllability, approximate controllability, optimal control, and optimal feedback control for several different kinds of fractional evolution equations. Optimality and relaxation of multiple control problems, described by nonlinear fractional differential equations with nonlocal control conditions in Banach spaces, are considered.

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Section: Introductionmentioning

confidence: 99%

A survey on fuzzy fractional differential and optimal control nonlocal evolution equations

Agarwal

Băleanu

Nieto

et al. 2018

Journal of Computational and Applied Mathematics

149

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“…In [18] positive or negative solutions to first-order fully fuzzy linear differential equations under generalized differentiability are studied. In [19] concreted solutions to fuzzy linear fractional differential equations under Riemann-Liouville H-differentiability is studied.…”

Section: Introductionmentioning

confidence: 99%

Numerical methods for solving fuzzy equations: A survey

Jafari

Razvarz

et al. 2021

Fuzzy Sets and Systems

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“…Furthermore, fractional differential equations in the fuzzy case [1] have been studied by many authors and they have been solved by various methods [6][7][8][9]. In [10], Hoa studied the fuzzy fractional differential equations under Caputo gH-differentiability, and in [11] Agarwal et al had a survey on mentioned problem to show the its relation with optimal control problems.…”

Section: Introductionmentioning

confidence: 99%

A Fuzzy Method for Solving Fuzzy Fractional Differential Equations Based on the Generalized Fuzzy Taylor Expansion

Allahviranloo

Noeiaghdam

et al. 2020

Mathematics

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In this field of research, in order to solve fuzzy fractional differential equations, they are normally transformed to their corresponding crisp problems. This transformation is called the embedding method. The aim of this paper is to present a new direct method to solve the fuzzy fractional differential equations using fuzzy calculations and without this transformation. In this work, the fuzzy generalized Taylor expansion by using the sense of fuzzy Caputo fractional derivative for fuzzy-valued functions is presented. For solving fuzzy fractional differential equations, the fuzzy generalized Euler’s method is introduced and applied. In order to show the accuracy and efficiency of the presented method, the local and global truncation errors are determined. Moreover, the consistency, convergence, and stability of the generalized Euler’s method are proved in detail. Eventually, the numerical examples, especially in the switching point case, show the flexibility and the capability of the presented method.

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Concreted solutions to fuzzy linear fractional differential equations

Cited by 39 publications

References 25 publications

A survey on fuzzy fractional differential and optimal control nonlocal evolution equations

A survey on fuzzy fractional differential and optimal control nonlocal evolution equations

Numerical methods for solving fuzzy equations: A survey

A Fuzzy Method for Solving Fuzzy Fractional Differential Equations Based on the Generalized Fuzzy Taylor Expansion

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