Abstract
In this paper, we study the fuzzy Laplace transforms introduced by the authors in (Allahviranloo and Ahmadi in Soft Comput. 14:235-243, 2010) to solve only first-order fuzzy linear differential equations. We extend and use this method to solve second-order fuzzy linear differential equations under generalized Hukuhara differentiability.
Highlights
In recent years, the theory of fuzzy differential equations (FDEs) has attracted widespread attention and has been rapidly growing
Allahviranloo et al proposed in [ ] a novel method for solving fuzzy linear differential equations, which its construction based on the equivalent integral forms of original problems under the assumption of strongly generalized differentiability
In, Allahviranloo and Ahmadi introduced in [ ] the fuzzy Laplace transform, which they used under the strongly generalized differentiability, in an analytic solution method for some first-order fuzzy differential equations (FDEs). In their main result the authors established the relation between the fuzzy Laplace transforms of a fuzzy function and its first derivative
Summary
The theory of FDEs has attracted widespread attention and has been rapidly growing. In , Allahviranloo and Ahmadi introduced in [ ] the fuzzy Laplace transform, which they used under the strongly generalized differentiability, in an analytic solution method for some first-order fuzzy differential equations (FDEs) In their main result the authors established the relation between the fuzzy Laplace transforms of a fuzzy function and its first derivative. They gave two numerical examples to illustrate the efficiency of the method, but these two examples are all first-order FDEs. ElJaoui et al Advances in Difference Equations (2015) 2015:66 derivative, with the purpose of solving second-order fuzzy linear differential equations under strongly generalized differentiability. All the limits are taken in the metric space (E, D), and at the end points of (a, b) and we consider only one-sided derivatives
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