AN EFFICIENT METHOD FOR SOLVING SINGULARLY PERTURBED TWO POINTS FRACTIONAL BOUNDARY-VALUE PROBLEMS

Abstract

In this thesis, we present numerical method for approximating the solutions of singularly perturbed two points boundary value problems in both cases: ordinary derivatives and fractional derivatives. We use the Caputo derivation for the fractional case. The method starts with solving the reduced problem then the boundary layer correction problem. A series method; namely, the Adomian decomposition method is used to solve the boundary layer correction problem, and then the series solution is approximated by the , - Pade’ approximation of order. Numerical and theoretical results are presented to show the efficiency of the method. Singularly perturbed problems arise frequently in many real-life applications and they are among the hardest numerical approximation problems. Fractional Calculus has been in the minds of mathematicians for 300 years and still contains many mesteries. In recent decades, fractional calculus has been the object of ever increasing interest, due to its applications in different areas of science and engineering