TY - JOUR

T1 - A boundary problem for the time-fractional Hallaire–Luikov moisture transfer equation with Hilfer derivative

AU - Al-Salti, Nasser

AU - Karimov, Erkinjon

AU - Kerbal, Sebti

N1 - Publisher Copyright:
© 2023, The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional.

PY - 2023/3

Y1 - 2023/3

N2 - 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.

AB - 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.

KW - Fourier series

KW - Hallaire–Luikov moisture transfer equation

KW - Hilfer derivative

KW - Multi-term time-fractional differential equation

KW - Multinomial Mittag–Leffler function

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U2 - 10.1007/s40314-023-02231-y

DO - 10.1007/s40314-023-02231-y

M3 - Article

AN - SCOPUS:85149007297

SN - 0101-8205

VL - 42

JO - Computational and Applied Mathematics

JF - Computational and Applied Mathematics

IS - 2

M1 - 94

ER -