Khalid HİLAL, Youssef ALLAOUİ, Karim GUİDA

EXISTENCE OF POSITIVE SOLUTIONS OF NONLINEAR FRACTIONAL QUADRATIC DIFFERENTIAL EQUATIONS

In this work, we prove the existence as well as approximations of the positive solutions for an initial value problem of nonlinear fractional quadratic dierential equations. We use some properties of the Mittag-Leer functions and its relationship with fractional calculus. Also we obtain some results regarding the existence of positive solutions using the Dhage iterative method embodied in a recent hybrid xed point theorem of Dhage in partially ordered normed linear spaces.

Keywords:

Fractional dierential equation hybrid systems, Dhage iterative method, Approximate positive solution,

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