The well-known Banach’s fixed point theorem asserts that ifD X, f is contractive and X, d is complete, then f has a unique fixed point inX. It is well known that the Banach contraction principle 1 is a very useful and classical tool in nonlinear analysis. In 1969, Boyd and Wong 2 introduced the notion ofΦ-contraction. A mapping f : X → X on a metric space is called Φ-contraction if there exists...

In this paper, we are concerned with a class of nonlinear implicit fractional di?erential equation adiscrete delay. By means the contraction mapping principle, prove existence unique solution.Then, investigate continuous dependence solution upon initial delay data and Ulamstability.

By employing the contraction mapping principle and applying Gronwall-Bellman's inequality, sufficient conditions are established to prove the existence and exponential stability of positive almost periodic solution for nonlinear impulsive delay model of hematopoiesis.

In this paper, we consider a class of nonlinear fuzzy integral equations of fractional order. The existence and uniqueness of solutions are established by the generalized Schauder theorem and contraction mapping principle.

An integrodifferential equation with fractional derivatives in the nonlinearities is studied in this article, and some sufficient conditions for existence and uniqueness of a solution for the equation are established by contraction mapping principle.

In this paper, we develop existence and uniqueness criteria to certain class of three point boundary value problems associated with third order nonlinear fuzzy differential equations, with the help of Green’s functions and contraction mapping principle.