A robust study upon fuzzy fractional 2D heat equation via semi-analytical technique

Abstract

This paper presents a novel semi-analytical approach to solve 2D fuzzy fractional heat equation which combines Shehu transform with Homotopy Perturbation Method. This method efficiently generates dual-bound solutions (lower and upper bounds) that precisely capture uncertainty inherent in fuzzy fractional systems. Proposed technique demonstrates remarkable advantages: it effectively handles the complexity of fractional derivatives while maintaining computational efficiency compared to traditional numerical methods. Through rigorous validation via using three distinct test illustrations, method’s accuracy and reliability are confirmed through comprehensive graphical and tabular analyses. The results disclose excellent agreement between approximate solutions and benchmark solutions, with confirmed theoretical and numerical convergence. Notably, this approach proves particularly valuable to handle problems where exact analytical solutions are unavailable or computationally difficult to fetch. This work not only provides a robust framework to solve fuzzy fractional PDEs but also offers practical insights for applications in heat transfer, diffusion processes, and other engineering systems involving uncertainty and memory effects. The method's efficiency and accuracy make it a compelling alternative to conventional numerical schemes for complex differential equations.