Conformable NE Transform: Theories, Methods and Applications

Abstract

In this study, we extend the NE transform formula to applicable fractional orders and examine several fascinating and fundamental properties of the transform. Additionally, we offer a comprehensive analytical solution for both linear and nonlinear fractional differential equations. We investigate the fractional Newell-Whitehead-Segel equation, a significant amplitude equation in physics, employing the conformable NE decomposition method. Furthermore, the method employed to derive approximate and analytical solutions for linear-nonlinear fractional partial differential equations integrates the Adomian decomposition method with the conformable NE transform. Ultimately, the results indicate that our proposed approach is effective and suitable for all situations concerning conformable fractional differential equations. This research supports SDG 4: Quality Education by advancing analytical methods in fractional calculus and mathematical modeling. © 2026 NSP.