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.
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PY - 2023/2/24
Y1 - 2023/2/24
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 - 2238-3603
VL - 42
JO - Computational and Applied Mathematics
JF - Computational and Applied Mathematics
IS - 2
M1 - 2
ER -