Analytical solutions of fractional PDEs via Banach space tensor product theory

In this paper, we propose a novel class of atomic solutions for fractional partial differential equations involving three independent variables, constructed through the framework of conformable derivatives. By leveraging the structural properties of Banach spaces and the theory of tensor product decomposition, we develop a rigorous analytical foundation for the formulation and validation of these solutions. The conformable derivative is employed for its compatibility with standard calculus rules, enabling efficient separation of variables and simplification of the solution process. Through analytical derivation and case analysis, we demonstrate the effectiveness, generality, and applicability of the proposed method in addressing high-dimensional fractional models.