Existence result for the fuzzy form of the equation governing the unsteady motion of solid particles in a fluid medium

The unsteady drag force in the equation governing the dynamics of small solid particles in the fluid medium appears as an integral Volterra operator in the equation, which is known as the history force. The history force has a kernel whose exact and general form is not known to date. In this article, the very general form of this equation is considered so that both the kernel of the history force and the fields affecting the particle motion can have a general linear or non-linear form. In the present work, the fuzzy form of this equation is proposed as a new method for uncertainty analysis of the problem. Using the Shoulder’s fixed point theorem in the semi-linear Banach space, it is proved that the fuzzy form of this equation has a solution.

کلیدواژه ها:

Implicit integro-differential equation ، GH-differentiability ، particle motion ، Schauder fixed point theorem