Solution of initial-value problem for linear third-order fuzzy differential equations
Yükleniyor...
Dosyalar
Tarih
2022
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
SPRINGER HEIDELBERG
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
Every real-world physical problem is inherently based on uncertainty. It is essential to model the uncertainty then solve, analyze and interpret the result one encounters in the world of vagueness. Generally, science and engineering problems are governed by differential equations. But the parameters, variables and initial conditions involved in the system contain uncertainty due to the lack of information in measurement, observations and experiment. However, It is necessary to develop a comprehensive approach for solving differential equations in an uncertain environment. The purpose of this work is to study and investigate the fuzzy solution of linear third-order fuzzy differential equations using the concept of strongly generalized Hukuhara differentiability (SGHD). To make our analysis possible, we apply the first and second differentiability up to the third-order fuzzy derivative of the fuzzy-valued function. Moreover, we develop an important result concerning the relationship between Laplace transform of fuzzy-valued function and third-order derivative. We construct an algorithm to determine a potential solution of linear third-order fuzzy initial-value problem using the Laplace transform technique. All these solutions are represented in terms of the Mittag-Leffler function involving a single series. Furthermore, we discuss the switching points of linear third-order differential equations and their corresponding solutions in fuzzy environments. To enhance the novelty of the proposed technique, some illustrative examples are presented as applications are analyzed to visualize and support theoretical results.
Açıklama
Anahtar Kelimeler
Switching Points, Fuzzy Initial-Value Problem, Strongly Generalized Differentiability, Fuzzy Laplace Transform, ittag-Leffler Function In Single Series
Kaynak
COMPUTATIONAL & APPLIED MATHEMATICS
WoS Q Değeri
Q1
Scopus Q Değeri
Q2
Cilt
41
Sayı
8
Künye
Akram, M., Muhammad, G., Allahviranloo, T., & Pedrycz, W. (2022). Solution of initial-value problem for linear third-order fuzzy differential equations. Computational and Applied Mathematics, 41(8), 1-31.
