TY - JOUR
T1 - Parameter-dependent fractional boundary value problems
T2 - analysis and approximation of solutions
AU - Marynets, Kateryna
AU - Pantova, Dona
PY - 2024
Y1 - 2024
N2 - We study a parameter-dependent non-linear fractional differential equation, subject to Dirichlet boundary conditions. Using the fixed point theory, we restrict the parameter values to secure the existence and uniqueness of solutions, and analyse the monotonicity behaviour of the solutions. Additionally, we apply a numerical-analytic technique, coupled with the lower and upper solutions method, to construct a sequence of approximations to the boundary value problem and give conditions for its monotonicity. The theoretical results are confirmed by an example of the Antarctic Circumpolar Current equation in the fractional setting.
AB - We study a parameter-dependent non-linear fractional differential equation, subject to Dirichlet boundary conditions. Using the fixed point theory, we restrict the parameter values to secure the existence and uniqueness of solutions, and analyse the monotonicity behaviour of the solutions. Additionally, we apply a numerical-analytic technique, coupled with the lower and upper solutions method, to construct a sequence of approximations to the boundary value problem and give conditions for its monotonicity. The theoretical results are confirmed by an example of the Antarctic Circumpolar Current equation in the fractional setting.
KW - approximation of solutions
KW - Caputo fractional differential equations
KW - fixed-point theorem
KW - fractional geophysical model
KW - upper and lower solutions
UR - http://www.scopus.com/inward/record.url?scp=85209893216&partnerID=8YFLogxK
U2 - 10.1080/00036811.2024.2426222
DO - 10.1080/00036811.2024.2426222
M3 - Article
AN - SCOPUS:85209893216
SN - 0003-6811
JO - Applicable Analysis
JF - Applicable Analysis
ER -