GENERALIZED MONOTONE ITERATIVE TECHNIQUES FOR CAPUTO FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH INITIAL CONDITION

摘要

The purpose of this work is to develop two Monotone Iterative Techniques for a nonlinear integro-differential initial value problem with Caputo derivative. Before proving the main results we will define different types of coupled lower and upper solutions. In the first theorem we will construct two natural sequences which converge uniformly and monotonically to coupled minimal and maximal solutions. In the second theorem we will construct two intertwined sequences which converge uniformly and monotonically to coupled minimal and maximal solutions. We also establish conditions for uniqueness of the solution. Finally, we present two examples that illustrate the results obtained.