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

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