Numerical Solutions of Non-Local Problem for fractional order differential equations

Abstract

The paper focuses on the study of problem- related to the linear second order boundary value problem (BVP). Three generalization styles are discussed. In the first, the second order BVP with non-local condition of the Dirichlet type is studied. In the second, the fractional order BVP is considered. In the third, the fractional order BVP with non-local condition is treated. The finite difference representation of the BVP is employed to reduce the problem into a system of algebraic equations, in addition, the implicit- explicit treatment to the nonlocal problems is introduced. In the implicit- explicit treatment the computational work is reduced considerably.