Application of Darbo-type generalized θ-Fℵ-contractions to the fractional order Lymphatic filariasis infection model

Abstract

This work presents a significant contribution to the field of mathematical analysis by introducing θ-Fℵ-contractions of Darbo-type. These newly introduced contractions serve as pivotal tools within our study. By employing these contractions, we systematically establish several pivotal fixed point theorems that allow us to guarantee the existence of fixed points in the Banach spaces. We construct particular examples in order to support the validity and effectiveness of our theoretical results. Moreover, we extend the utility of our established theorems by applying them to solve real-world problems. Specifically, we direct our attention to exploring the existence of solutions to the fractional order Lymphatic filariasis infection model.

Keywords

• Fixed point
• Contraction
• Fractional derivative
• Lymphatic filariasis infection model
• Measure of noncompactness