A Unified Transform Approach for Analyzing Fractional Differential Models with Diverse Fractional Operators

Abstract

This study explores a class of fractional mathematical models through a comprehensive generalized integral transform technique. The models examined include fractional representations of Newton’s cooling phenomenon, population dynamic governed by a logistic-type growth law, and a system describing blood alcohol concentration. To formulate these models, various fractional differentiation schemes are utilized, including Caputo, CF, modified ABC, and CPC derivatives. Closed form analytical solutions are derived using the generalized integral transform (GIT) framework, and the corresponding behaviors are illustrated numerically for different fractional orders. The obtained results align with established classical outcomes in limiting cases and further highlight the adaptability and robustness of the proposed transform method when applied to systems involving multiple fractional operators. These findings emphasize the potential of the generalized transform approach in capturing memory-dependent dynamics arising in real-world processes described by fractional differential equations. © 2026 NSP.