DHAGE ITERATION METHOD FOR GENERALIZED QUADRATIC FRACTIONAL INTEGRAL EQUATIONS WITH MAXIMA

In this paper we prove an existence and an approximation result for a generalized nonlinear quadratic fractional integral equation with maxima of mixed type. An algorithm for the solutions is developed and it is shown that the sequence of successive approximations starting with a lower or an upper solution converges monotonically to the solution of the related quadratic fractional integral equation with maxima under some suitable mixed hybrid conditions. We base our main results on the Dhage iteration principle embodied in a recent hybrid fixed point theorem of Dhage (2014) in a partially ordered normed linear space. A couple of numerical examples are also furnished to illustrate the hypotheses and abstract theory developed in the paper.