Laplace Transform Solutions for Heat and Mass Transfer Problem using Caputo-Fabrizio Fractional Derivative

The novelty of this study lies in the development of closed-form analytical solutions for coupled heat and mass transfer processes using the Caputo–Fabrizio fractional derivative, a non-singular operator that realistically captures memory-dependent diffusion without the limitations of classical fractional models. Unlike existing works that mainly focus on integer-order or singular-kernel fractional formulations, this research introduces a non-singular, exponential-kernel fractional framework to investigate transient thermal and solutal transport in viscous media. More exactly, this study investigates the analytical solutions of coupled heat and mass transfer problems in a time-fractional framework employing the Caputo–Fabrizio fractional derivative operator. The model considers transient transport phenomena in a viscous fluid medium under generalized thermal and concentration gradients. The use of the Caputo–Fabrizio derivative, characterized by its non-singular exponential kernel, enables the realistic modeling of memory effects without mathematical singularities inherent in classical fractional operators. The governing equations are transformed into the Laplace domain to derive closed-form expressions for temperature and concentration distributions. The inverse Laplace transform is then applied to obtain the time-domain solutions. The influence of the fractional parameter on heat and mass transfer characteristics is examined in detail, highlighting the role of fractional-order differentiation in controlling diffusion and relaxation behaviors. Graphical results demonstrate that decreasing fractional order slows the rate of thermal and solutal diffusion, reflecting stronger memory effects. The findings offer valuable insights into the design and optimization of fractional-order heat and mass transfer systems applicable in thermal engineering, material processing, and porous media transport.