TY - JOUR
N2 - We introduce the Sobolev-type multi-term μ-fractional evolution with generalized fractional orders with respect to another function. We make some applications of the generalized Laplace transform. In the sequel, we propose a novel type of Mittag-Leffler function generated by noncommutative linear bounded operators with respect to the given function and give a few of its properties. We look for the mild solution formula of the Sobolev-type evolution equation by building on the aforementioned Mittag-Leffler-type function with the aid of two different approaches. We share new special cases of the obtained findings.
L1 - http://www.czasopisma.pan.pl/Content/130025/PDF/BPASTS_2024_72_2_3456.pdf
L2 - http://www.czasopisma.pan.pl/Content/130025
PY - 2024
IS - 2
EP - e149170
DO - 10.24425/bpasts.2024.149170
KW - degenerate evolution equation
KW - Sobolev
KW - generalized Laplace transform
KW - fractional derivative with respect to another function
KW - Mittag-Leffler type function
A1 - Aydin, Mustafa
A1 - Mahmudov, Nazim
VL - 72
DA - 13.01.2024
T1 - Some applications of the generalized Laplace transform and the representation of a solution to Sobolev-type evolution equations with the generalized Caputo derivative
SP - e149170
UR - http://www.czasopisma.pan.pl/dlibra/publication/edition/130025
T2 - Bulletin of the Polish Academy of Sciences Technical Sciences
ER -