The Fuzzy Sumudu Decomposition Method for Solving Differential Equations in an Imprecise Context

Abstract

This paper presents the fuzzy Sumudu decomposition technique (FSDM) as a novel method for dealing with differential equations that contain uncertainty. The FSDM method allows for the direct solution of fuzzy differential equations, eliminating the need to convert them into their classical counterparts, which is a need in conventional methodologies. This is achieved by analysing the equations using a novel fuzzy arithmetic approach. By employing FSDM, we generate solutions using infinite series that gradually converge towards the exact solutions for the specific problems being studied. This approach offers a reliable and powerful tool for dealing with differential equations in a fuzzy setting, enabling us to understand and handle the inherent uncertainty inside the system. An illustrative numerical example is presented to showcase the potential and practicality of the FSDM. This case serves as an illustration of how the technique can be employed to tackle realworld difficulties. This illustration showcases the efficacy of the FSDM (Fuzzy Set Differential Method) in effectively solving fuzzy differential equations and generating accurate results. This study contributes to the subject of differential equations by introducing the fuzzy Sumudu decomposition methodology as an alternative strategy for dealing with uncertainty. The FSDM approach offers a novel and efficient technique for resolving fuzzy differential equations through the redefinition of the issue and the use of fuzzy arithmetic. This is illustrated with a numerical example.