Hybrid of Block-pulse and orthonormal Bernstein functions for fractional differential equations

Abstract

Differential equations of fractional order have been the focus of many studies due to their frequent appearance in various applications in fluid mechanics, biology, physics, and engineering. In general, it is not easy to derive the analytical solutions to most of these equations. Therefore, it is vital to develop some reliable and efficient techniques to solve fractional differential equations. A numerical method for solving fractional differential equations is proposed in this paper. The method is based on a hybrid of Block-pulse and orthonormal Bernstein functions. Convergence analysis is given, and numerical examples are introduced to illustrate the effectiveness and simplicity of the method.

Keywords

• fractional differential equations
• hybrid functions
• block-pulse functions
• bernstein polynomials