  This paper introduces a novel approach to address inherent limitations in the
Residual Power Series (RPS) method and its variants with Laplace-like
transforms when applied to solving time-fractional differential equations.
Existing methods, while successful, often require computationally expensive
calculations for the coefficients of the series solution. To overcome this
limitation, we propose a new framework for the RPS method that utilizes a
general integral transform. This framework incorporates an explicit formula for
calculating coefficients, thereby eliminating repetitive computations and
streamlining the solution process. Moreover, it offers a universally applicable
approach, remaining compatible with various RPS methods that employ
Laplace-like transform variants.
