Type-2 fuzzy fractional derivatives

被引：96
作者：
Mazandarani, Mehran [1 ]
Najariyan, Marzieh
机构：
[1] Ferdowsi Univ Mashhad, Dept Elect Engn, Mashhad, Iran
来源：
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2014年 / 19卷 / 07期
关键词：
Type-2 fuzzy sets; Type-2 Hukuhara difference; Type-2 fuzzy fractional differential equations; Caputo type-2 fuzzy fractional derivative; Riemann-Liouville type-2 fuzzy fractional derivative; H-2-differentiability; DIFFERENTIAL-EQUATIONS;
D O I：
10.1016/j.cnsns.2013.11.003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we introduce two definitions of the differentiability of type-2 fuzzy number-valued functions of fractional order. The definitions are in the sense of Riemann-Liouville and Caputo derivative of order beta is an element of (0, 1), and based on type-2 Hukuhara difference and H-2-differentiability. The existence and uniqueness of the solutions of type-2 fuzzy fractional differential equations (T2FFDEs) under Caputo type-2 fuzzy fractional derivative and the definition of Laplace transform of type-2 fuzzy number-valued functions are also given. Moreover, the approximate solution to T2FFDE by a Predictor-Evaluate-Corrector-Evaluate (PECE) method is presented. Finally, the approximate solutions of two examples of linear and nonlinear T2FFDEs are obtained using the PECE method, and some cases of T2FFDEs applications in some sciences are presented. (C) 2013 Elsevier B. V. All rights reserved.
引用
收藏
页码：2354 / 2372
页数：19
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