Generalized Monotone Iterative Techniques for Fractional Differential Equations with Boundary Conditions.

摘要

In this dissertation we develop generalized iterative technique for three different types of fractional boundary value problems: (i) Riemann Liouville fractional periodic boundary value problem of order q, 0 q 1; (ii) Caputo fractional boundary value problem of order alpha, 1 alpha 2; and (iii) Caputo fractional periodic boundary value problem of order q, 0 q 1, for which the forcing function is the sum of an increasing and a decreasing function. For each type of problem we need the appropriate comparison results and coupled lower and upper solutions in order to develop natural monotone sequences, or intertwined monotone sequences. The sequences converge uniformly and monotonically to coupled minimal and maximal solutions.