TY - JOUR
T1 - Quasilinearization method for finite systems of nonlinear rl fractional differential equations
AU - Denton, Zachary
AU - Ramírez, Juan Diego
PY - 2020/1/1
Y1 - 2020/1/1
N2 - In this paper the quasilinearization method is extended to finite systems of Riemann-Liouville fractional differential equations of order 0 < q < 1. Existence and comparison results of the linear Riemann-Liouville fractional differential systems are recalled and modified where necessary. Using upper and lower solutions, sequences are constructed that are monotonic such that the weighted sequences converge uniformly and quadratically to the unique solution of the system. A numerical example illustrating the main result is given.
AB - In this paper the quasilinearization method is extended to finite systems of Riemann-Liouville fractional differential equations of order 0 < q < 1. Existence and comparison results of the linear Riemann-Liouville fractional differential systems are recalled and modified where necessary. Using upper and lower solutions, sequences are constructed that are monotonic such that the weighted sequences converge uniformly and quadratically to the unique solution of the system. A numerical example illustrating the main result is given.
KW - Fractional differential systems
KW - Lower and upper solutions
KW - Quasilinearization method
UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85098113654&origin=inward
UR - https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=85098113654&origin=inward
U2 - 10.7494/OpMath.2020.40.6.667
DO - 10.7494/OpMath.2020.40.6.667
M3 - Article
SN - 1232-9274
VL - 40
SP - 667
EP - 683
JO - Opuscula Mathematica
JF - Opuscula Mathematica
IS - 6
ER -