The solution of fuzzy Hybrid differential equations

Subject Areas : Statistics

Nayyereh Shahryari ¹ , tofigh allahviranloo ^{2 *} , Saeid Abbasbandy ³

1 - گروه ریاضی، دانشکده علوم پایه، واحد علوم و تحقیقات، دانشگاه آزاد اسلامی، تهران، ایران
2 - گروه ریاضی، دانشکده علوم پایه، واحد علوم و تحقیقات، دانشگاه آزاد اسلامی، تهران، ایران
3 - گروه ریاضی کاربردی، دانشکده علوم پایه، دانشگاه بین المللی امام خمینی (ره)، قزوین، ایران

Received: 2020-12-21 Accepted : 2021-10-02 Published : 2024-01-18

Keywords: معادلات دیفرانسیل هیبریدی فازی: مشتق پذیری تعمیم: روش اویلر فازی,

Abstract :

In this paper we are going to solve the hybrid fuzzy differential equation (HFDE) by Fuzzy Euler’s method (FEM) under generalized differentiability. In this regard, we showed that the solutions obtained by fuzzy Euler method (FEM) are convergent to the exact solution to the problem and this convergence is established in all points of the definition range. On the other hand, we introduced the Allocating method and solved the hybrid fuzzy differential equation for 1-cut, and then assign the right and left spreads to the resulting equation. As a result, the equation is converted in to two equations of linear differential in term of these spreads, and in the end, with the solution of this system, we obtained the left and right spreads. Therefore, the fuzzy solution is obtained. Finally, we introduced three sets of solutions for the hybrid fuzzy differential equation, for more illustration several numerical examples are solved.

References:


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