Asian Research Journal of Mathematics

This paper presents an efficient numerical approach based on Lagrange interpolation polynomials for solving higher-order nonlinear fractional boundary value problems. The proposed Lagrange Interpolation TransformMethod (LITM), formulated using the Caputo fractional derivative, effectively captures the memory effects inherent in fractional systems. An explicit computational framework is developed, in which the problem is reduced to a system of algebraic equations using Chebyshev collocation points and Lagrange basis functions. The applicability of the method is demonstrated through several nonlinear and higher-order test problems, and the results obtained are compared with existing techniques such as the ChebyshevWavelet Method (CWM) and the Optimal Homotopy Asymptotic Method (OHAM), with the comparisons showing improved accuracy and stable convergence. It is also observed that the fractional solutions converge to their corresponding integer-order solutions as the order approaches unity, confirming the consistency of the formulation. The method is simple, computationally efficient, and applicable to a wide class of fractional and classical boundary value problems.