Fuzzy Laplace transforms

Abstract

In this paper we propose a fuzzy Laplace transform and under the strongly generalized differentiability concept, we use it in an analytic solution method for some fuzzy differential equations (FDEs). The related theorems and properties are proved in detail and the method is illustrated by solving some examples.

Aumann Fuzzy Improper Integral and Its Application to Solve Fuzzy Integro-Differential Equations by Laplace Transform Method

“…To achieve this goal, we first introduce the Aumann fuzzy improper integral concept, which we utilize instead of the Riemann fuzzy improper integral used in [10,[12][13][14].…”

“…To prove Theorem 18, one can adopt the proof in [10] using Aumann fuzzy improper integral instead of Riemann fuzzy improper integral. …”

“…This concept of improper fuzzy Riemann integral was later exploited by Allahviranloo and Ahmadi in [10] to introduce the fuzzy Laplace transform, which they used to solve some first-order fuzzy differential equations (FDEs). Salahshour and Allahviranloo gave in [11] some applications of fuzzy Laplace transform and studied sufficient conditions ensuring its existence.…”

Fuzzy Sumudu Transform for Fuzzy nth- Order Derivative and Solving Fuzzy Ordinary Differential Equations

“…In the field of fuzzy integral transforms Allahviranloo and Ahmadi in [6] have proposed the fuzzy Laplace transforms for solving first-order fuzzy differential equations strongly generalized Hdifferentiability concept. Salahshour and Allahviranloo in [7] have expressed the fuzzy Laplace transform and then some of its well-known properties are investigated.…”

Soution of fuzzy initial value problems by fuzzy Laplace transform

“…In 2008, T.Allahviranloo et al [22] solved Nth-order fuzzy linear differential equations.The fuzzy Laplace transforms for solving first order fuzzy differential equations under H-differentiability have proposed by Allahviranloo and Ahmadi [2].A new method for solving fuzzy linear differential equations obtained by T. Allahviranloo, S.Abbasbandy, and S. Salahshour , A.Hakimzadeh [21]. The fuzzy Laplace transforms to solve second-order FIVPs under generalized H-differentiability applied by S.Salahshour, T.Allahviranloo [3].The fuzzy approximate solutions of second order fuzzy linear boundary value problems found by Xiaobin Guo,Dequan Shang and Xiaoquan. [25] Strongly generalized differentiability was introduced and studied by Bede et al [5,6] the existence and uniqueness theorem of solution of Nth-order fuzzy differential equations under generalized differentiability was studied by S Salahshour [18].In 2015,Patel and Desai [15] find solution of variable coefficient fuzzy initial value problems by properties of Linear Transformtion.The strongly generalized derivative is defined for a larger class of fuzzy valued function than the H-derivative, and fuzzy differential equations can have solutions which have a decreasing length of their support.…”