Investigation of Some Properties of Solutions for Some Two-Point Boundary Value Fractional Differential Equations

Abstract

In this thesis, we investigated some properties of solutions for a class of nonlinear boundary value fractional differential equations in a given Sobolev space. Some fixed point theorems were applied to obtain the existence and uniqueness solutions of the problem. In addition, the famous LeggetWilliams fixed point theorem and Banach contraction mapping principle were used to obtain Other qualitative properties of solutions such as nonnegativity(positive) solutions. Furthermore, various stability characterizations such as Hyers-Ulam-Rassias, Mittag-Leffler, Lyapunov-like stability of the class of problem were studied using some fixed point theorems. Quantitatively, we applied monotone iterative technique due to Picard to obtain an approximate solution to the problem. Equally, by using Laplace transform, we obtained a solution to a particular class of our problem. Also, the Homotopy perturbation method was used as a numerical technique to obtain numerical and graphical solutions of the class of problem. Lastly, as an application, fractional duffing Oscillator was used to investigate some ground motions. X