TY - JOUR
T1 - Generalized extension of the quasilinearization method for Riemann-Liouville fractional differential equations
AU - Denton, Zachary
PY - 2014/1/1
Y1 - 2014/1/1
N2 - Existence and comparison results of the linear and nonlinear Riemann-Liouville fractional differential equations of order q, 0 < q < 1, are recalled and modified where necessary. Using upper and lower solutions, an extension of the generalized quasilinearization method is developed for decomposed nonlinear fractional differential equations of order q containing generalized convex, concave, and nondifferentiable partitions. Quadratic convergence, and generalizations thereof, to the unique solution is proved via weighted sequences.
AB - Existence and comparison results of the linear and nonlinear Riemann-Liouville fractional differential equations of order q, 0 < q < 1, are recalled and modified where necessary. Using upper and lower solutions, an extension of the generalized quasilinearization method is developed for decomposed nonlinear fractional differential equations of order q containing generalized convex, concave, and nondifferentiable partitions. Quadratic convergence, and generalizations thereof, to the unique solution is proved via weighted sequences.
UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84908152428&origin=inward
UR - https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=84908152428&origin=inward
M3 - Article
SN - 1056-2176
VL - 23
SP - 333
EP - 350
JO - Dynamic Systems and Applications
JF - Dynamic Systems and Applications
IS - 2-3
ER -