Dhage iteration method for IVPs of nonlinear first order hybrid fractional functional differential equations
In this paper, we discuss a couple of nonlinear hybrid fractional functional differential equations involving a delay and explain the power of a new successive iteration method in applications. In particular, we prove the existence and uniqueness results for approximate solutions of an initial value problem of the first-order nonlinear hybrid fractional functional differential equation via the construction of an algorithm. The main results rely on the Dhage iteration method embodied in the recent hybrid fixed point principles of Dhage (2014) in a partially ordered normed linear space. Examples are also furnished to illustrate the hypotheses and the abstract results of this paper.