Opuscula Math. 40, no. 6 (2020), 667-683
https://doi.org/10.7494/OpMath.2020.40.6.667

Opuscula Mathematica

# Quasilinearization method for finite systems of nonlinear RL fractional differential equations

Zachary Denton
Juan Diego Ramírez

Abstract. 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.

Keywords: fractional differential systems, lower and upper solutions, quasilinearization method.

Mathematics Subject Classification: 34A08, 34A34, 34A45.

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• Communicated by Marek Galewski.
• Revised: 2020-09-13.
• Accepted: 2020-10-25.
• Published online: 2020-12-01. 