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 stab...

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Bibliographic Details
Published in:Acta mathematica vietnamica 2017-12, Vol.42 (4), p.675-700
Main Authors: Long, Hoang Viet, Kim Son, Nguyen Thi, Thanh Tam, Ha Thi, Yao, Jen-Chih
Format: Article
Language:English
Subjects:
Differential equations
Infinity
Mathematics
Mathematics and Statistics
Nonlinear equations
Stability
Uncertainty
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Summary: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.
ISSN:0251-4184
2315-4144
DOI:10.1007/s40306-017-0207-2