Numerical analysis of some deformable fractional problems based on the perturbation method

Abstract

This paper presents solutions for several deformable fractional problems. Initially, by applying Banach's contraction principle, the existence and uniqueness of the fixed point are established. Then, using the reductive perturbation method, it is shown that a solution can be determined that closely approximates the exact result, without needing specific information about the solution required by the d'Alembert method. Our findings could assist in achieving a better alignment between theoretical and numerical outcomes, and in gaining insights into the characteristics of certain deformable fractional problems.