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Ulam Stability for Fractional Partial Integro-Differential Equation with Uncertainty

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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 ∞ = [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.

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Acknowledgments

This research is funded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.02-2015.08.

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Authors and Affiliations

  1. Faculty of Information Technology, People’s Police University of Technology and Logistics, Bac Ninh, Vietnam

    Hoang Viet Long

  2. Department of Mathematics, Hanoi University of Education, Hanoi, Vietnam

    Nguyen Thi Kim Son

  3. Department of Basic Sciences, University of Transport Technology, Hanoi, Vietnam

    Ha Thi Thanh Tam

  4. Center for General Education, China Medical University, Taichung, 40402, Taiwan

    Jen-Chih Yao

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  1. Hoang Viet Long
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  2. Nguyen Thi Kim Son
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  3. Ha Thi Thanh Tam
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  4. Jen-Chih Yao
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Correspondence to Hoang Viet Long.

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Long, H.V., Kim Son, N.T., Thanh Tam, H.T. et al. Ulam Stability for Fractional Partial Integro-Differential Equation with Uncertainty. Acta Math Vietnam 42, 675–700 (2017). https://doi.org/10.1007/s40306-017-0207-2

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  • DOI: https://doi.org/10.1007/s40306-017-0207-2

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