<p>This article focuses on inverse problem for Hallaire-Luikov moisture transfer equation involving Hilfer fractional derivative in time. Hallaire-Luikov equation is used to study heat and mass transfer in capillary-porous bodies. Spectral expansion method is used to find the solution of the inverse problem. By imposing certain conditions on the functions involved and utilizing certain properties of multinomial Mittag-Leffler function, it is shown that the solution to the equation, known as the inverse problem, is regular and unique. Moreover, the inverse problem exhibits ill-posedness in the sense of Hadamard. The article ends with an example to demonstrate these theoretical findings.</p>

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Existence and Uniqueness Results for Generalized Non-local Hallaire-Luikov Moisture Transfer Equation

  • Asim Ilyas,
  • Salman A. Malik,
  • Kamran Suhaib

摘要

This article focuses on inverse problem for Hallaire-Luikov moisture transfer equation involving Hilfer fractional derivative in time. Hallaire-Luikov equation is used to study heat and mass transfer in capillary-porous bodies. Spectral expansion method is used to find the solution of the inverse problem. By imposing certain conditions on the functions involved and utilizing certain properties of multinomial Mittag-Leffler function, it is shown that the solution to the equation, known as the inverse problem, is regular and unique. Moreover, the inverse problem exhibits ill-posedness in the sense of Hadamard. The article ends with an example to demonstrate these theoretical findings.