ON SOLUTIONS TO ITERATIVE DIFFERENTIAL EQUATIONS

We present existence and uniqueness of solution for iterative differential equation $y'=f(x,y,y(g(y)))$ using Picard's iteration method by imposing some conditions on $f$ and $g$. These conditions are sufficient conditions (not necessary conditions) for existence of solution. Furthermore, examples are provided to clarify existence and uniqueness of solution.

Positive solutions of nonlinear fourth order iterative differential equations with two-point and integral boundary conditions

This paper provides sufficient conditions to guarantee the existence, uniqueness and continuous dependence of positive solutions of a nonlinear fourth order iterative differential equations with two-point and integral boundary conditions. The main arguments are based on the Schauder fixed point theorem to prove the existence of a positive solution. As an application, we given an example to illustrate the obtained results.

Existence and approximation of solutions of fractional order iterative differential equations

In this paper, we investigate existence and approximation of solutions of fractional order iterative differential equations by virtue of nonexpansive mappings, fractional calculus and fixed point methods. Three existence theorems as well as convergence theorems for a fixed point iterative method designed to approximate these solutions are obtained in two different work spaces via Chebyshev’s norm, Bielecki’s norm and β norm. Finally, an example is given to illustrate the obtained results.