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Positive and negative definite comparison results for nonlinear  q -th fractional differential equations of Riemann-Liouville type are derived without requiring Hölder continuity assumption. Monotone iterative method is then developed to a class of nonlinear boundary value problems for fractional differential equations, using coupled upper and lower solutions. Existence of the multiplicity solutions for the nonlinear fractional differential equations is presented.

The multiplicity solutions for nonlinear fractional differential equations of Riemann-Liouville type