Some new operational matrices and its application to fractional order Poisson equations with integral type boundary constrains

Abstract

Enormous application of fractional order partial differential equations (FPDEs) subjected to some constrains in the form of nonlocal boundary conditions motivated the interest of many scientists around the world. The prime objective of this article is to find approximate solution of a general FPDEs subject to nonlocal integral type boundary conditions on both ends of the domain. The proposed method is based on spectral method. We construct some new operational matrices which have the ability to handle integral type non-local boundary constrains. These operational matrices can be effectively applied to convert the FPDEs together with its integral types boundary conditions to easily solvable matrix equation. The accuracy and efficiency of proposed method are demonstrated by solving some bench mark problems. The proposed method has the ability to solve non-local FPDEs with high accuracy and low computational cost. Different aspects of presented approach are compared with two other recently developed methods, Haar wavelets collocation method and a family of collocation methods which are based on Radial base functions. It is observed that the proposed method is highly accurate, robust, efficient and stable as compared to these methods.