Boundary value problems for nonlinear fractional integro-differential equations: Theoretical and numerical results

Abstract

This article is devoted to both the theoretical and numerical study of boundary-value problems for nonlinear fractional integro-differential equations. Positivity and uniqueness results for the problem are provided and proved. Two monotone sequences of upper and lower solutions which converge uniformly to the unique solution of the problem are constructed using the method of lower and upper solutions. Sufficient numerical examples are discussed to corroborate the theory presented herein. © 2012 Al-Mdallal.