Euler method for solving hybrid fuzzy differential equation

Abstract

In this paper, we study the numerical method for solving hybrid fuzzy differential using Euler method under generalized Hukuhara differentiability. To this end, we determine the Euler method for both cases of H-differentiability. Also, the convergence of the proposed method is studied and the characteristic theorem is given for both cases. Finally, some numerical examples are given to illustrate the efficiency of the proposed method under generalized Hukuhara differentiability instead of suing Hukuhara differentiability.

Fuzzy functional integro-differential equations under generalized H-differentiability

“…Also, as a very important generalization and development related to the subject of the present paper is in the field of fuzzy sets, i.e., fuzzy calculus and fuzzy differential equations under generalized Hukuhara derivative. Recently, several works as e.g., [5][6][7][8][9][10][11][12][13][14][15], [18][19][20], [2,23,29,30,42], [38][39][40], [48][49][50][51].…”

A Hukuhara approach to the study of hybrid fuzzy systems on time scales

“…We say that D + ∆ V (t, u(t)) ∈ R is the upper ∆-Dini derivative of V (t, u(t)) with respect to (2), if for any given ε > 0 there exists a right neighborhood U ε of t ∈ T such that…”

Switching Point Solution of Second-Order Fuzzy Differential Equations Using Differential Transformation Method

“…Fuzzy differential equations are solved using many methods, such as differential or fuzzy inclusion [10][11][12], the extension principle and characterization theorem [13][14][15], and artificial neural networks [16]. Numerical methods such as the differential transformation method [17,18], extension of numerical solution methods for ordinary differential equations (ODEs) [19][20][21][22][23][24], interactive derivatives [25], multistep methods [26], and Runge-Kutta (RK) methods [27] are also applied to solving these equations. The metric properties of fuzzy functions are studied in [28,29].…”