Fuzzy Differential Equations in Various Approaches

Gomes, Luciana Takata; Barros, Laécio Carvalho de; Bede, Barnabás

doi:10.1007/978-3-319-22575-3

Cited by 52 publications

(36 citation statements)

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“…For convenience, we give some definitions and introduce the necessary notations and lemmas (see e. g., monographs [16,17,18,19] and references contained therein) which will be used in the following sections.…”

Section: Preliminariesmentioning

confidence: 99%

Existence of Solutions to Boundary Value Problems for a Class of Nonlinear Fuzzy Fractional Differential Equations

Wang¹,

Sun²,

Han³

2017

AAN

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In this paper, we investigate the existence and uniqueness of solution to boundary value problems for a class of nonlinear fuzzy factional differential equations involving the fuzzy gHfractional Caputo derivative. By means of the Schauder fixed point theorem in semi-linear spaces and integral inequality technique, some qualitative results of solutions are obtained. An example is provided from which new results are found.

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Section: Preliminariesmentioning

confidence: 99%

Existence of Solutions to Boundary Value Problems for a Class of Nonlinear Fuzzy Fractional Differential Equations

Wang¹,

Sun²,

Han³

2017

AAN

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“…The literature on numerical solutions of integro-differential equations (IDEs) is vast. We used the Sumudu decomposition method [6][7][8] to solve linear and nonlinear fuzzy integral equations (FIEs). The method gives more realistic series solutions that converge very rapidly in physical problems.…”

Section: Introductionmentioning

confidence: 99%

Sumudu Decomposition Method for Solving Fuzzy Integro-Differential Equations

Kang

Iqbal

Habib

et al. 2019

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Different results regarding different integro-differentials are usually not properly generalized, as they often do not satisfy some of the constraints. The field of fuzzy integro-differentials is very rich these days because of their different applications and functions in different physical phenomena. Solutions of linear fuzzy Volterra integro-differential equations (FVIDEs) are more generalized and have better applications. In this report, the Sumudu decomposition method (SDM) was used to find the solution to some linear and nonlinear fuzzy integro-differential equations (FIDEs). Some examples are given to show the validity of the presented method.

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“…The generalized Hukuhara derivative for fuzzy functions was introduced and studied in [4]. For detailed overview of theory of fuzzy differential equations, we refer the readers to consult the monographs [5,6].…”

Section: Introductionmentioning

confidence: 99%

On Darboux-Type Differential Inclusions with Uncertainty

2019

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In this article we prove the existence results for solutions of the Darboux-type problems in fuzzy partial differential inclusions with local conditions of integral types. We present two problems involving open and closed level sets of a given fuzzy mapping. In the first case fuzzy differential inclusion has been transformed into an equivalent Darboux-type problem for partial differential equations and then using the Tychonoff fixed point theorem we prove the existence result for this crisp case. For the second case we use Nadler's fixed point theorem and selection theorem of Kuratowski-Ryll-Nardzewski to find the solution of given differential inclusions problem. We furnish an example to validate our results.

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Fuzzy Differential Equations in Various Approaches

Cited by 52 publications

References 0 publications

Existence of Solutions to Boundary Value Problems for a Class of Nonlinear Fuzzy Fractional Differential Equations

Existence of Solutions to Boundary Value Problems for a Class of Nonlinear Fuzzy Fractional Differential Equations

Sumudu Decomposition Method for Solving Fuzzy Integro-Differential Equations

On Darboux-Type Differential Inclusions with Uncertainty

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