Novel Fuzzy Contractions and Applications to Engineering Science

Abstract

The article outlines a creative approach by fusing ideas from fuzzy contractions, graph mappings, and Kannan mappings to create a brand-new notion known as “Kannan-graph-fuzzy contraction”. This combination of concepts makes it possible to create a unique framework for resolving real-world issues controlled by nonlinear models. It is anticipated that using Kannan-graph-fuzzy contractions will offer a fresh approach to discussing solution existence in situations where these ideas overlap. This strategy might have a significant impact on a lot of real-world applications, proving how practical multidisciplinary techniques are for tackling issues in the real world originating from technology and engineering. The article includes several illustrated examples based on computer simulations, making the results more explicit.

Keywords

• fixed point
• fractional-differential equation
• equation of motion
• fuzzy-Kannan mapping
• fuzzy metric
• directed graph