TY - JOUR
T1 - Maximum principle and its application for the nonlinear time-fractional diffusion equations with Cauchy-Dirichlet conditions
AU - Borikhanov, Meiirkhan
AU - Kirane, Mokhtar
AU - Torebek, Berikbol T.
N1 - Funding Information:
M. Kirane was supported by the Ministry of Education and Science of the Russian Federation (Agreement No. 02.a03.21.0008). M. Borikhanov and B.T. Torebek were financially supported by a grant no. AP05131756 from the Ministry of Science and Education of the Republic of Kazakhstan.
Funding Information:
M. Kirane was supported by the Ministry of Education and Science of the Russian Federation (Agreement No. 02.a03.21.0008 ). M. Borikhanov and B.T. Torebek were financially supported by a grant no. AP05131756 from the Ministry of Science and Education of the Republic of Kazakhstan .
Publisher Copyright:
© 2018 Elsevier Ltd
PY - 2018/7
Y1 - 2018/7
N2 - In this paper, a maximum principle for the one-dimensional sub-diffusion equation with Atangana–Baleanu fractional derivative is formulated and proved. The proof of the maximum principle is based on an extremum principle for the Atangana–Baleanu fractional derivative that is given in the paper, too. The maximum principle is then applied to show that the initial–boundary-value problem for the linear and nonlinear time-fractional diffusion equations possesses at most one classical solution and this solution continuously depends on the initial and boundary conditions.
AB - In this paper, a maximum principle for the one-dimensional sub-diffusion equation with Atangana–Baleanu fractional derivative is formulated and proved. The proof of the maximum principle is based on an extremum principle for the Atangana–Baleanu fractional derivative that is given in the paper, too. The maximum principle is then applied to show that the initial–boundary-value problem for the linear and nonlinear time-fractional diffusion equations possesses at most one classical solution and this solution continuously depends on the initial and boundary conditions.
KW - Atangana–Baleanu derivative
KW - Fractional differential equation
KW - Maximum principle
KW - Nonlinear problem
KW - Riemann–Liouville derivative
KW - Sub-diffusion equation
UR - http://www.scopus.com/inward/record.url?scp=85042176907&partnerID=8YFLogxK
U2 - 10.1016/j.aml.2018.01.012
DO - 10.1016/j.aml.2018.01.012
M3 - Article
AN - SCOPUS:85042176907
SN - 0893-9659
VL - 81
SP - 14
EP - 20
JO - Applied Mathematics Letters
JF - Applied Mathematics Letters
ER -