Abstract
In this article, we aim to define a universal set consisting of the subscripts of the fuzzy differential equation (5) except the two elements and , subsets of that universal set are defined according to certain conditions. Then, we use the constructed universal set with its subsets for suggesting an analytical method which facilitates solving fuzzy initial value problems of any order by using the strongly generalized H-differentiability. Also, valid sets with graphs for solutions of fuzzy initial value problems of higher orders are found.
Highlights
The concept of the fuzzy derivative was first introduced by Chang and Zadeh (1), it was followed up by Dubios and Prade (2), and Puri and Ralescu (3)
7e t 2 cos Discussion In this paper we suggest a method for finding analytical solutions for FIVPs of higher orders by using fuzzy Laplace transform by the concept of strongly generalized H-differentiability
This method depends on introducing the subscripts which appear in the fuzzy differential equation as a universal set, and defining other subsets which form a partition of that universal set
Summary
The concept of the fuzzy derivative was first introduced by Chang and Zadeh (1), it was followed up by Dubios and Prade (2), and Puri and Ralescu (3). The fuzzy Laplace transform (FLT) is proposed to solve first order fuzzy differential equations (FDEs) by using the strongly generalized differentiability concept (4), and some of wellknown properties of the fuzzy Laplace transform were investigated. A formula of the fuzzy Laplace transform of the nthorder derivative was initially introduced in terms of the number of derivatives in form (ii) by Mohammad Ali ( 6), and Haydar and Mohammad Ali (7), it was followed by introducing another formula for the fuzzy Laplace transform on fuzzy nth-order derivative by concept of the strongly generalized differentiability (8). We extend the proposed method by Mohammed (18), for solving nth-order classical differential equations by the classical Laplace transform to solve nth-order FDEs by FLT under the strongly generalized H-differentiability. We introduce theorem and some corollaries that help us in solving nth-order FDEs
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