TY - JOUR
T1 - Direct and inverse problems with a dynamical condition for the sub-diffusion equation involving the Hilfer-Prabhakar integral-differential operator
AU - Karimov, Erkinjon
AU - Kerbal, Sebti
AU - Turdiev, Khurshidjon
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Springer-Verlag Italia S.r.l., part of Springer Nature 2025.
PY - 2026/2
Y1 - 2026/2
N2 - A unique solvability of direct and inverse problems with dynamical conditions in space variables for a sub-diffusion equation involving the Hilfer-Prabhakar integral-differential operator has been proved. Proofs are done with the application of the spectral expansion method, based on the solution of the Cauchy problem for the corresponding fractional differential equation and using certain properties of the bivariate Mittag-Leffler function.
AB - A unique solvability of direct and inverse problems with dynamical conditions in space variables for a sub-diffusion equation involving the Hilfer-Prabhakar integral-differential operator has been proved. Proofs are done with the application of the spectral expansion method, based on the solution of the Cauchy problem for the corresponding fractional differential equation and using certain properties of the bivariate Mittag-Leffler function.
KW - Hilfer-Prabhakar integral-differential operator
KW - bivariate Mittag-Leffler function
KW - dynamical condition
KW - sub-diffusion equation
UR - https://www.scopus.com/pages/publications/105025351732
UR - https://www.scopus.com/pages/publications/105025351732#tab=citedBy
U2 - 10.1007/s12215-025-01351-0
DO - 10.1007/s12215-025-01351-0
M3 - Article
AN - SCOPUS:105025351732
SN - 0009-725X
VL - 75
JO - Rendiconti del Circolo Matematico di Palermo
JF - Rendiconti del Circolo Matematico di Palermo
IS - 1
M1 - 35
ER -