Atomic solutions to Bateman–Burgers type equation via tensor products

This study presents a novel approach for solving fractional partial differential equations, notably the fractional Bateman–Burgers type equation, by employing the tensor product of Banach spaces. This study proposes a novel analytical method that transcends traditional techniques like separation of variables, enabling precise atomic solutions to complex fractional equations. Central to our approach is the utilization of the α -conformable fractional derivative, which enhances the analytical framework for addressing such complex equations. Our findings provide solutions to the fractional Bateman–Burgers type equation and illustrate the potential of integrating advanced mathematical theories to solve complex problems across various scientific disciplines. This work promises to pave new pathways for research in fractional calculus and its application in both theoretical and applied mathematics. • Tensor products of Banach spaces used to solve fractional PDEs. • Solutions for fractional Bateman–Burgers type equation via a conformable derivative. • Advanced mathematical theories applied to complex equations. • Initial conditions’ role in shaping solution landscape. • Effects of diffusion and convection analyzed using solution surfaces.