A numerical scheme for problems in fractional calculus

Abstract

In this paper, a new numerical method for solving the fractional differential equations with boundary value problems is presented. The method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The Riemann-Liouville fractional integral operator for hybrid functions is given. This operator is then utilized to reduce the solution of the boundary value problems for fractional differential equations to a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

Keywords

• Hybrid functions
• fractional-order differential equations
• block-pulse
• Bernoulli polynomials
• Caputo derivative
• numerical solution