Fuzzy Laplace transform based on the Henstock integral and its applications in discontinuous fuzzy systems

2019 ◽  
Vol 358 ◽  
pp. 1-28
Author(s):  
Zengtai Gong ◽  
Yadong Hao
Keyword(s):  
Laplace Transform ◽  
Fuzzy Systems ◽  
Henstock Integral ◽  
Fuzzy Laplace Transform

scholarly journals Soution of fuzzy initial value problems by fuzzy Laplace transform

10.29007/pnq2 ◽  
2018 ◽  
Author(s):  
Komal Patel ◽  
Narendrasinh Desai
Keyword(s):  
Laplace Transform ◽  
Initial Value Problem ◽  
Level Sets ◽  
Initial Value Problems ◽  
Initial Value ◽  
Generalized Differentiability ◽  
Strongly Generalized Differentiability ◽  
Fuzzy Laplace Transform ◽  
Mathematica Software

In this paper we propose a fuzzy Laplace transform to solve fuzzy initial value problem under strongly generalized differentiability concept. The fuzzy Laplace transform of derivative was used to solve Nth-order fuzzy initial value problem. To illustrate applicability of proposed method we plot graphs for different values of r -level sets by using Mathematica Software.

scholarly journals On Solutions of Linear Fractional Differential Equations with Uncertainty

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
T. Allahviranloo ◽  
S. Abbasbandy ◽  
M. R. Balooch Shahryari ◽  
S. Salahshour ◽  
D. Baleanu
Keyword(s):  
Differential Equations ◽  
Laplace Transform ◽  
Fractional Differential Equations ◽  
Fractional Differential ◽  
Fuzzy Laplace Transform ◽  
Fuzzy Fractional Differential Equations ◽  
Linear Fractional Differential Equations

The solutions of linear fuzzy fractional differential equations (FFDEs) under the Caputo differentiability have been investigated. To this end, the fuzzy Laplace transform was used to obtain the solutions of FFDEs. Then, some new results regarding the relation between some types of differentiability have been obtained. Finally, some applicable examples are solved in order to show the ability of the proposed method.

scholarly journals SOLVING THE FUZZY INITIAL VALUE PROBLEM WITH NEGATIVE COEFFICIENT BY USING FUZZY LAPLACE TRANSFORM

2020 ◽  
Vol 35 (1) ◽  
pp. 201
Author(s):  
Hülya Gültekin Çitil
Keyword(s):  
Laplace Transform ◽  
Initial Value Problem ◽  
Negative Coefficient ◽  
Initial Value ◽  
Generalized Differentiability ◽  
Comparison Results ◽  
Fuzzy Laplace Transform

In this paper, the fuzzy initial value problem with negative coefficient is solved by using fuzzy Laplace transform and generalized differentiability. The solutions are found and the comparison results are given.

A study on the fuzzy parabolic Volterra partial integro-differential equations

2021 ◽  
Vol 40 (1) ◽  
pp. 1639-1654
Author(s):  
E. Qahremani ◽  
T. Allahviranloo ◽  
S. Abbasbandy ◽  
N. Ahmady
Keyword(s):  
Differential Equations ◽  
Laplace Transform ◽  
Existence And Uniqueness ◽  
Parabolic Type ◽  
Fuzzy Mathematics ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Differentiability Of Solutions ◽  
Fuzzy Laplace Transform ◽  
Fuzzy Solutions

This paper is concerned with aspects of the analytical fuzzy solutions of the parabolic Volterra partial integro-differential equations under generalized Hukuhara partial differentiability and it consists of two parts. The first part of this paper deals with aspects of background knowledge in fuzzy mathematics, with emphasis on the generalized Hukuhara partial differentiability. The existence and uniqueness of the solutions of the fuzzy Volterra partial integro-differential equations by considering the type of [gH - p]-differentiability of solutions are proved in this part. The second part is concerned with the central themes of this paper, using the fuzzy Laplace transform method for solving the fuzzy parabolic Volterra partial integro-differential equations with emphasis on the type of [gH - p]-differentiability of solution. We test the effectiveness of method by solving some fuzzy Volterra partial integro-differential equations of parabolic type.

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