A computational strategy based on the residual power series method with the help of the Laplace transforms

In this article with the external source terms, we have successfully developed approximate solutions of one-dimensional fuzzy fractional partial differential equations using the Laplace residual power series method. The generalized algorithm of the proposed technique is formulated under the Caputo fractional derivative operator. To verify the results, several illustrative examples have been solved to demonstrate the effectiveness of the methodology. Graphs representing the solutions at various fractional orders are plotted and compared with the solutions at the integer-order derivative. The graphical analysis confirms a strong agreement between the fractional solutions and the exact solution. The tables show that the solutions obtained by the present technique are more accurate compared to those obtained by the finite difference method. furthermore, the plots of approximate solutions approach those at the classical order ( $\gamma =1$) as the fractional order $\gamma$ approaches to its integer value. Therefore, we conclude that fractional calculus effectively captures the global dynamics of problems involving fuzzy concepts.