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Ulam Stability for Fractional Partial Integro-Differential Equation with Uncertainty
Hoang Viet Long
,
Nguyen Thi Kim Son
,
Ha Thi Thanh Tam
,
Jen-Chih Yao
Abstract
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 $J_{\infty} = [0,\infty) \times [0,\infty)$. 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.