##### Title: A New Monotone Iteration Principle in the Theory of Nonlinear Fractional Differential Equations

##### Pages: 130-143

##### Cite as:

Bapurao C. Dhage, A New Monotone Iteration Principle in the Theory of Nonlinear Fractional Differential Equations, Int. J. Anal. Appl., 8 (2) (2015), 130-143.#### Abstract

In this paper the author proves the algorithms for the existence as well as approximations of the solutions for the initial value problems of nonlinear fractional diﬀerential equations using the operator theoretic techniques in a partially ordered metric space. The main results rely on the Dhage iteration principle embodied in the recent hybrid ﬁxed point theorems of Dhage (2014) in a partially ordered normed linear space and the existence and approximations of the solutions of the considered nonlinear fractional diﬀerential equations are obtained under weak mixed partial continuity and partial Lipschitz conditions. Our hypotheses and existence and approximation results are also well illustrated by some numerical examples.

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