A Modified Laplace Fractional Residual Power Series Technique for Handling Non-linear Models of Fuzzy Partial Differential Equations of Fractional Order (Contemporary Mathematics, 2025)
In this work, the time-nonlinear fuzzy fractional order partial differential equations with a suitable fuzzy initial data in the presence of the Caputo differential operator are analytically and numerically investigated using the extended Laplace fractional residual power series scheme. The analytic-approximate fuzzy solutions have been extracted under generalized Hukuhara partial differentiability via fuzzy Laplace transform, along with the simulation of the fractional residual power series strategy. The suggested approach is demonstrated to be effective in solving three non-linear fractional-order initial value problems under uncertainty; the graphical and numerical impacts demonstrate the algorithm’s accuracy and ability. Quantitative and graphical presentations of the influence of fractional-motion and uncertain levels demonstrate the agreement between the fuzzy exact and approximate solutions. The outcomes reveal that the congruence between the lower and upper portions of uncertain levels depictions of the fuzzy solutions, and the convex symmetric triangular fuzzy number is fulfilled. As a result, the proposed scheme is a practical and straightforward mathematical instrument for obtaining fuzzy approximation and exact analytical solutions to time-nonlinear Fuzzy Fractional Order Partial Differential Equations (FFOPDEs) of the specified type.
Keywords: Fuzzy Fractional Order Partial Differential Equations (FFOPDEs), generalized Hukuhara partial differentiability, Laplace fractional residual power series method