EXISTENCE AND APPROXIMATION OF SOLUTIONS FOR GENERALIZED QUADRATIC FRACTIONAL INTEGRAL EQUATIONS

Abstract

In this paper we prove the existence as well as approximation of the solutions for a nonlinear generalized quadratic fractional integral equation 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 under some suitable mixed hybrid conditions. The existence of minimal and maximal solutions and the related integral inequalities are also proved under certain monotonic conditions. We base our main results on the Dhage iteration principle embodied in a recent hybrid fixed point theorem of Dhage (2014) in partially ordered normed linear spaces. A couple of examples are also provided to illustrate the hypotheses and abstract theory developed in the paper.