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

Articles in Press

Document Type : Research Paper

Authors

1 Faculty of Mathematics‎, ‎Statistics and Computer sciences‎, ‎University of Tabriz‎, ‎Tabriz‎, ‎Iran.

2 Department of Mechanical Engineering‎, ‎Ahar branch‎, ‎Islamic Azad University‎, ‎Ahar‎, ‎Iran.

Abstract

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 Shoulder's fixed point theorem in the semi-linear Banach space, it is proved that the fuzzy form of this equation has a solution.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 11 January 2025

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History

  • Receive Date: 05 October 2024
  • Revise Date: 24 December 2024
  • Accept Date: 31 December 2024

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