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Well-posedness and ill-posedness results for backward problem for fractional pseudo-parabolic equation | Journal of Applied Mathematics and Computing Skip to main content
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Well-posedness and ill-posedness results for backward problem for fractional pseudo-parabolic equation

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Abstract

In this paper, we study a pseudo-parabolic equation with the Caputo fractional derivative. By applying the properties of Mittag–Leffler functions and the method of eigenvalue expansion, under a suitable definition of mild solution of our problem, we obtain the existence result and \(L^p\) regularity of the mild solution by using some Sobolev embeddings. Finally, we also give some examples to illustrate the proposed method.

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Acknowledgements

This work is supported by Thu Dau Mot University.

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Authors and Affiliations

  1. Division of Applied Mathematics, Thu Dau Mot University, Thu Dau Mot, Binh Duong Province, Vietnam

    Le Dinh Long & Nguyen Huy Tuan

  2. Faculty of Information Technology, Macau University of Science and Technology, Macau, 999078, China

    Yong Zhou

  3. Faculty of Mathematics and Computational Science, Xiangtan University, Hunan, 411105, China

    Yong Zhou

  4. Department of Applied Mathematics, Bharathiar University, Coimbatore, 641046, India

    Rathinasamy Sakthivel

  5. Faculty of Mathematics and Computer Science, University of Science, Vietnam National University, 227 Nguyen Van Cu, District 5, Ho Chi Minh City, Vietnam

    Nguyen Huy Tuan

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  1. Le Dinh Long
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  2. Yong Zhou
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  3. Rathinasamy Sakthivel
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  4. Nguyen Huy Tuan
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Correspondence to Nguyen Huy Tuan.

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Long, L.D., Zhou, Y., Sakthivel, R. et al. Well-posedness and ill-posedness results for backward problem for fractional pseudo-parabolic equation. J. Appl. Math. Comput. 67, 175–206 (2021). https://doi.org/10.1007/s12190-020-01488-4

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