A boundary problem for the time-fractional Hallaire–Luikov moisture transfer equation with Hilfer derivative

Nasser Al-Salti, Erkinjon Karimov*, Sebti Kerbal

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We aim to prove a unique solvability of a boundary-value problem with Dirichlet conditions for the Hallaire–Luikov moisture transfer equation involving generalized fractional derivative (Hilfer derivative) in time. The formal solution to the problem has been obtained in a series form using the method of spectral expansion. Imposing certain conditions on given functions and using certain properties of the multinomial Mittag–Leffler function, we prove a uniform convergence of corresponding infinite series. Moreover, a number of properties of the multinomial Mittag–Leffler function in some particular cases are also presented. Finally, an example solution is provided to illustrate the obtained results.

Original languageEnglish
Article number94
JournalComputational and Applied Mathematics
Issue number2
Publication statusPublished - Mar 2023


  • Fourier series
  • Hallaire–Luikov moisture transfer equation
  • Hilfer derivative
  • Multi-term time-fractional differential equation
  • Multinomial Mittag–Leffler function

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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