Opuscula Math. 31, no. 3 (2011), 327-339
http://dx.doi.org/10.7494/OpMath.2011.31.3.327

Opuscula Mathematica

# Monotone iterative technique for finite systems of nonlinear Riemann-Liouville fractional differential equations

Z. Denton
A. S. Vatsala

Abstract. Comparison results of the nonlinear scalar Riemann-Liouville fractional differential equation of order $$q$$, $$0 \lt q \leq 1$$, are presented without requiring Hölder continuity assumption. Monotone method is developed for finite systems of fractional differential equations of order $$q$$, using coupled upper and lower solutions. Existence of minimal and maximal solutions of the nonlinear fractional differential system is proved.

Keywords: fractional differential systems, coupled lower and upper solutions, mixed quasimonotone property.

Mathematics Subject Classification: 34A08, 24A34.

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• Z. Denton
• University of Louisiana Lafayette, Department of Mathematics, Lafayette, LA 70504 USA
• A. S. Vatsala
• University of Louisiana Lafayette, Department of Mathematics, Lafayette, LA 70504 USA
• Revised: 2010-11-15.
• Accepted: 2010-12-01.