Open AccessQuasilinearization method for finite systems of nonlinear RL fractional differential equations
Author(s) -
Zachary Denton,
J. D. Ramírez
Publication year - 2020
Publication title -
rocznik akademii górniczo-hutniczej im. stanisława staszica. opuscula mathematica/opuscula mathematica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 16
eISSN - 2300-6919
pISSN - 1232-9274
DOI - 10.7494/opmath.2020.40.6.667
Subject(s) - mathematics , monotonic function , nonlinear system , quadratic growth , order (exchange) , mathematical analysis , differential equation , physics , finance , quantum mechanics , economics
In this paper the quasilinearization method is extended to finite systems of Riemann-Liouville fractional differential equations of order \(0\lt q\lt 1\). 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.