Mathematics and Computer Applications - Sciene

In this thesis, we introduce a modified approach for solving fractional order boundary value problems. This approach is given by applying the Riesz-Feller operator to obtain a modified finite difference equation, which is symmetric to the equation of fractional boundary value problems. Also, the main objective of this work is to study the existence and uniqueness theorem of solutions of the fractional boundary value problems, and to present their proof depending on Schauder fixed point theorem for fractional order integral operator.

In this work, we consider two Monte Carlo methods for evaluating the n-dimensional integrals for bounded integrand. Statistical properties of these methods are illustrated and unified. The supported number of trials to estimate the integrals, confidence interval and the efficiency for each method were derived theoretically and assessed practically.

In this work, we consider the Weibull distribution of two parameters for its importance in statistics and its applications. Mathematical and statistical properties of Weibull distribution are considered, moments and higher moments are illustrated and unified.