Fixed Point Results with Applications to Fractional Differential Equations of Anomalous Diffusion

Abstract

The main objective of this manuscript is to define the concepts of F-(⋏,h)-contraction and (α,η)-Reich type interpolative contraction in the framework of orthogonal F-metric space and prove some fixed point results. Our primary result serves as a cornerstone, from which established findings in the literature emerge as natural consequences. To enhance the clarity of our novel contributions, we furnish a significant example that not only strengthens the innovative findings but also facilitates a deeper understanding of the established theory. The concluding section of our work is dedicated to the application of these results in establishing the existence and uniqueness of a solution for a fractional differential equation of anomalous diffusion.