Fixed Point Theory on Ordered Sets with Applications to Mathematical Physics Problems


General Information

12-MAT2895-02

Fixed Point Theory on Ordered Sets with Applications to Mathematical Physics Problems

Mathematics And Physics

Applied Mathematics

The goal of this project is to develop and provide new mathematical tools on nonlinear analysis that will be used to the study of various problems arising in physics and engineering. We will mainly focus on the existence and uniqueness of fixed points for single and multi-valued mappings on metric spaces endowed with a partial order. The obtained results will be extended to more general spaces: • Gauge spaces, • Fuzzy metric spaces. • Probabilistic metric spaces. • Partial metric spaces. The obtained fixed point theorems will be used to the study of various nonlinear problems: • Fractional differential equations. • Elastic beam equations. • Impulsive differential inclusions. This project will provide an exciting opportunity for us to develop and make further advances on applied mathematics in King Saud University and for all the Kingdom of Saudi Arabia.

The main objectives of this project are the following: 1. To develop and provide new mathematical tools on nonlinear analysis and fixed point theory. 2. To study the existence and uniqueness of solutions to nonlinear problems arising in physics and engineering:

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