Fuzzy multiquadric radial basis functions for solving fuzzy partial differential equations

Dirbaz, M.; Allahviranloo, Tofigh

doi:10.1007/s40314-019-0942-1

Cited by 4 publications

(1 citation statement)

References 21 publications

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“…In other words, fuzzy PDEs are usually used to deal with multi-dimensional dynamic systems of realistic problems in fuzzy environments [6] and have been developed more rapidly with the great expansion of research fields such as physical science, population dynamics, station elasticity, and so on. See, for example, [2,[7][8][9][10][11][12] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Initial Value Problems of Fuzzy Fractional Coupled Partial Differential Equations with Caputo gH-Type Derivatives

Zhang

Lan

2022

Fractal Fract

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The purpose of this paper is to investigate a class of initial value problems of fuzzy fractional coupled partial differential equations with Caputo gH-type derivatives. Firstly, using Banach fixed point theorem and the mathematical inductive method, we prove the existence and uniqueness of two kinds of gH-weak solutions of the coupled system for fuzzy fractional partial differential equations under Lipschitz conditions. Then we give an example to illustrate the correctness of the existence and uniqueness results. Furthermore, because of the coupling in the initial value problems, we develop Gronwall inequality of the vector form, and creatively discuss continuous dependence of the solutions of the coupled system for fuzzy fractional partial differential equations on the initial values and ε-approximate solution of the coupled system. Finally, we propose some work for future research.

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Section: Introductionmentioning

confidence: 99%

Initial Value Problems of Fuzzy Fractional Coupled Partial Differential Equations with Caputo gH-Type Derivatives

Zhang

Lan

2022

Fractal Fract

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A fuzzy solution of wave equation by FFS‐transform

Allahviranloo

Ghobadi

Matinfar

2020

Numerical Methods Partial

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In this paper, we introduce a fuzzy Fourier sine transform decomposition as an analytical solution of a fuzzy wave equation under generalized Hukuhara partial differentiability. Since the fuzzy transforms have already been proven to solve several problems in different fields, they propel us to utilize them as a practical and appropriate way to solve the wave equation. The theorems and properties are demonstrated in detail, then the efficiency of the proposed approach is confirmed through solving several examples.

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Fuzzy Multi Quadric Radial Basis Functions for Solving Fractional Boundary Value Problems

Dirbaz

2021

Advances in Intelligent Systems and Computing

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Fuzzy multiquadric radial basis functions for solving fuzzy partial differential equations

Cited by 4 publications

References 21 publications

Initial Value Problems of Fuzzy Fractional Coupled Partial Differential Equations with Caputo gH-Type Derivatives

Initial Value Problems of Fuzzy Fractional Coupled Partial Differential Equations with Caputo gH-Type Derivatives

A fuzzy solution of wave equation by FFS‐transform

Fuzzy Multi Quadric Radial Basis Functions for Solving Fractional Boundary Value Problems

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