Efficient semianalytical investigation of a fractional model describing human cornea shape

Abstract

Purpose: This study presents a novel application of the semianalytical residual power series method to investigate a one-dimensional fractional anisotropic curvature equation describing the human cornea, the outermost layer of the eye. The fractional boundary value problem, involving the fractional derivative of curvature, poses challenges that conventional methods struggle to address. Methods: The analytical results are obtained by utilizing the simple and efficient residual power series method. The proposed method is accessible to researchers in all medical fields and is extendable to various models in disease spread and control. Results: The derived solution is a crucial outcome of this study. Through the application of the proposed method to the corneal shape model, an explicit formula for the curvature profile is obtained. To validate the solution, direct comparisons are made with numerical solutions for the integer case and other analytical solutions available in the literature for the fractional case. Conclusion: Our findings highlight the potential of the proposed method to significantly contribute to the diagnosis and treatment of various ophthalmological conditions.