Ulam Stability for Fractional Partial Integro-Differential Equation with Uncertainty

In this paper, the solvability of Darboux problems for nonlinear fractional partial integro-differential equations with uncertainty under Caputo gH-fractional differentiability is studied in the infinity domain J ∞ = [0, ∞ ) × [0, ∞ ). New concepts of Hyers-Ulam stability and Hyers-Ulam-Rassias stability for these problems are also investigated through the equivalent integral forms. A computational example is presented to demonstrate our main results.