Fractional Novel Analytical Method (FNAM): An Improved Innovative Numerical Scheme to Solve Fractional Differential‐Difference Equations

ABSTRACT This study develops the Fractional Novel Analytical Method (FNAM), a Taylor‐series–oriented approach for constructing approximate analytical solutions of NFDΔEs prevalent in control, integrability studies, and arithmetic modeling. Grounded in the Caputo fractional derivative, the method attains rapid convergence of truncated series and eliminates dependence on Adomian polynomial decompositions, multiplier methods, auxiliary parameters, perturbative schemes, and transform operators. Testing on three well‐known NFDΔEs with fractional order and combined delay terms reveal that FNAM secures high‐fidelity approximations with limited series terms. The method proceeds by extracting a direct coefficient recurrence from the NFDΔE.A short convergence proof is outlined. Across all test cases, few‐term truncations suffice to reach high accuracy, with absolute errors below those of ADTM/HATM/PIA/MHLM under matched truncation depth and reduced runtime due to analytic coefficient recurrences. Graphical overlays against exact benchmarks show strong concordance. In concert, the analytical framework and numerical results show that FNAM provides a robust and resource‐efficient solution strategy for NFDΔEs, with competitive accuracy achieved through minimal machinery. The method's transform‐independent design, elementary calculus basis, and reliable convergence characteristics make it an attractive option for a wide class of fractional models.