Fractional partial differential equations are essential for modeling complex dynamical phenomena across scientific disciplines. However, most remain difficult to solve analytically. This paper proposes the Spectral Homotopy Perturbation Method (SHPM), combining the Homotopy Perturbation Method with Chebyshev pseudo-spectral transformations. The method provides rigorous convergence proofs via the Banach Fixed Point Theorem and explicit error bounds. Numerical applications to the time-fractional diffusion equation and fractional thin film flow equation demonstrate accuracy with maximum absolute errors ranging from 10⁻⁴ to 10⁻¹⁵. Comparative analysis shows SHPM achieves superior accuracy with reasonable computational effort, making it an efficient tool for fractional problems in applied mathematics and engineering.................... Keywords:..............Fractional Partial Differential Equations, Spectral Homotopy Perturbation Method, Homotopy Perturbation Method, Chebyshev Pseudo-Spectral Method, Convergence Analysis, Diffusion Equation, Fluid Dynamics