University of Tabriz Computational Methods for Differential Equations 2345-3982 14 1 2026 11 01 Existence result for the fuzzy form of the equation governing the unsteady motion of solid particles in a fluid medium 23 35 19078 10.22034/cmde.2024.63793.2862 EN Masoumeh Zeinali Faculty of Mathematics‎, ‎Statistics and Computer sciences‎, ‎University of Tabriz‎, ‎Tabriz‎, ‎Iran. Ghiyam Eslami Department of Mechanical Engineering‎, ‎Ahar branch‎, ‎Islamic Azad University‎, ‎Ahar‎, ‎Iran. Journal Article 2024 10 05 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. https://cmde.tabrizu.ac.ir/article_19078_abc43ac36aef73c84511961125f5d5ba.pdf