TY - JOUR
T1 - Approximation Approach to the Fractional BVP with the Dirichlet Type Boundary Conditions
AU - Marynets, Kateryna
AU - Pantova, Dona
PY - 2022
Y1 - 2022
N2 - We use a numerical-analytic technique to construct a sequence of successive approximations to the solution of a system of fractional differential equations, subject to Dirichlet boundary conditions. We prove the uniform convergence of the sequence of approximations to a limit function, which is the unique solution to the boundary value problem under consideration, and give necessary and sufficient conditions for the existence of solutions. The obtained theoretical results are confirmed by a model example.
AB - We use a numerical-analytic technique to construct a sequence of successive approximations to the solution of a system of fractional differential equations, subject to Dirichlet boundary conditions. We prove the uniform convergence of the sequence of approximations to a limit function, which is the unique solution to the boundary value problem under consideration, and give necessary and sufficient conditions for the existence of solutions. The obtained theoretical results are confirmed by a model example.
KW - Approximation of solutions
KW - Brouwer degree
KW - Dirichlet boundary conditions
KW - Fractional differential equations
UR - http://www.scopus.com/inward/record.url?scp=85137218776&partnerID=8YFLogxK
U2 - 10.1007/s12591-022-00613-y
DO - 10.1007/s12591-022-00613-y
M3 - Article
AN - SCOPUS:85137218776
SN - 0971-3514
JO - Differential Equations and Dynamical Systems
JF - Differential Equations and Dynamical Systems
ER -