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Inverse problem for the Atangana–Baleanu fractional differential equation

  • Santosh Ruhil ORCID logo and Muslim Malik ORCID logo EMAIL logo
Published/Copyright: March 31, 2023

Abstract

In this manuscript, we examine a fractional inverse problem of order 0 < ρ < 1 in a Banach space, including the Atangana–Baleanu fractional derivative in the Caputo sense. We use an overdetermined condition on a mild solution to identify the parameter. The major strategies for determining the outcome are a direct approach using the Volterra integral equation for sufficiently regular data. For less regular data, an optimal control approach uses Euler–Lagrange (EL) equations for the fractional order control problem (FOCP) and a numerical approach for solving FOCP. At last, a numerical example is provided in the support of our results.

Award Identifier / Grant number: 02011/23/2021 NBHM (R.P)/R&DII/8776

Funding statement: The work of the first author is supported by the National Board of Higher Mathematics (NBHM) under project grant no. 02011/23/2021 NBHM (R.P)/R&DII/8776.

Acknowledgements

The authors would like to express their sincere thanks to the associate editor and the anonymous reviewers for their valuable comments and suggestions.

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Received: 2022-03-29
Revised: 2022-11-26
Accepted: 2023-01-23
Published Online: 2023-03-31
Published in Print: 2023-10-01

© 2023 Walter de Gruyter GmbH, Berlin/Boston

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