Some novel mathematical analysis on a corneal shape model by using Caputo fractional derivative

In this article, we solve a fractional boundary value problem (FBVP) for modeling the human corneal shape dynamics. We use the Caputo fractional derivative having singular type kernel. We propose some novel simulations to prove the existence of a unique solution of the given FBVP. The numerical solution of the proposed problem is derived by using a polynomial least squares method. We do a number of graphical observations at various values of the given model parameters along with the orders of considered fractional derivative. The main motivation of this research article is to specify the possibilities that the corneal shape may slightly differ to the shapes which were investigated in various past studies at any fixed set of available parameters. The given model was not generalized before by using any fractional derivative which is the main reason for the proposal of this study as well as the novelty of the work.

Automated summary

This article investigates a fractional boundary value problem for modeling human corneal shape dynamics, proposing novel simulations to prove the existence of a unique solution and deriving the numerical solution using a polynomial least squares method.