Fuzzy Solutions of Fuzzy Fractional Parabolic Integro Differential Equations

This work primarily investigates the numerical solution of fuzzy fractional parabolic integro-differential equations of the Volterra type with the time derivative defined in the Caputo sense using the fuzzy Adomian decomposition method. Fuzzy fractional partial integro-differential equations pose significant mathematical challenges due to the interplay between fuzziness and fractional-order dynamics, while at the same time, there is a growing need for accurate and efficient methods to model real-world phenomena involving uncertainty in physics, biology, and engineering. The fuzzy Adomian decomposition method provides an alternative approach for obtaining approximate fuzzy solutions, and its applicability to such equations has not been studied in detail previously in the literature. Furthermore, existence and uniqueness theorems for the fuzzy fractional partial integro-differential equation are established by considering the differentiability type of the solution. The accuracy and efficiency of the proposed method are demonstrated through a series of numerical experiments.