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On backward fractional pseudo parabolic equation: Regularization by quasi-boundary value method, convergence rates

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Abstract

This paper is concerned with the backward problem of recovering initial value for a homogeneous time-space fractional pseudo parabolic differential equation. Since the problem is ill-posed, a version of modified quasi boundary value method is used as the method of regularization for obtaining stable approximations. Error analysis and parameter choice strategies are done for both a priori and a posteriori cases. It is shown that, the order of the convergence rate can exceed \(\frac{2}{3}.\) Hence, the obtained rate improves upon the previously known rates of order \(\frac{2}{3}\) for the a priori case, and \(\frac{1}{2}\) for the a posteriori case for the considered problem.

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Acknowledgements

The author sincerely thanks the reviewer for meticulously reading the manuscript and providing valuable comments. The author is supported by the postdoctoral fellowship of the TIFR Centre for Applicable Mathematics, Bangalore.

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  1. TIFR Centre for Applicable Mathematics, Bangalore, 560 065, India

    Subhankar Mondal

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  1. Subhankar Mondal
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Correspondence to Subhankar Mondal.

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Communicated by A K Nandakumaran.

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Mondal, S. On backward fractional pseudo parabolic equation: Regularization by quasi-boundary value method, convergence rates. Proc Math Sci 134, 5 (2024). https://doi.org/10.1007/s12044-023-00772-0

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  • DOI: https://doi.org/10.1007/s12044-023-00772-0

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