A New Method for Solving Fuzzy Bernoulli Differential Equation

Abstract

Abstract In this paper, the solution of fuzzy Bernoulli differential equation (FBDE) of the form u'(t)+p(t) u(t)=q(t) u^n(t), u(0)=u0, is investigated in which p(t) and q(t)  are real continues functions,  u(t)=(x(t),y(t),z(t)) is LR fuzzy function, u0  is LR fuzzy number . First, n th power of LR fuzzy number is defined then using generalized Hukuhara difference and differentiability, [i.gH]-differentiability and [ii.gH]-differentiability are described. Thereafter, by solving 1-cut FBDE, determining the sign of x(t), p(t), q(t) and defining a theorem,   u(t) as a LR fuzzy function is calculated. Finally, numerical examples verify the effectiveness of the proposed method.