Analysis of Fractional-Order Biological Model via A Novel Semi-Analytical Approach

This study presents a hybrid methodology that combines a novel fractional integral transform with the Fractional Differential Transform Method (FDTM) to solve fractional differential equations (FDEs). The proposed approach exploits the transform’s ability to handle fractional-order systems efficiently by improving solution convergence and preserving Mittag-Leffler-type behavior. The new method provides solutions for both linear and nonlinear problems with reduced computational effort compared to other techniques such as the Adomian Decomposition Method and Variational Iteration Method, which require multiple integrations and differentiations. In contrast, the proposed method avoids such computations by utilizing the integral transform. The efficacy of this hybrid approach is demonstrated through the analysis of a fractional-order prey-predator model with a single carrying capacity. Series solutions for various fractional orders are obtained and validated through numerical comparison with existing methods, showing that the proposed technique achieves similar accuracy while requiring fewer computational steps. Graphical illustrations highlight its practical utility in solving non-linear FDEs, underscoring the advantages of the hybrid methodology in fractional modeling.