Hybrid Bernstein Block–Pulse functions for solving system of fractional integro-differential equations

ABSTRACT

This paper deals with the numerical solution of system of fractional integro-differential equations. In this work, we approximate the unknown functions based on the hybrid Bernstein Block–Pulse functions, in conjunction with the collocation method. We introduce the Riemann–Liouville fractional integral operator for the hybrid Bernstein Block–Pulse functions. This operator will be approximated by the Gauss quadrature formula with respect to the Legendre weight function and then it is utilized to reduce the solution of the fractional integro-differential equations to a system of algebraic equations. This system can be easily solved by any usual numerical methods. The existence and uniqueness of the solution have been discussed. Moreover, the convergence analysis of this algorithm will be shown by preparing some theorems. Numerical experiments are presented to show the superiority and efficiency of proposed method in comparison with some other well-known methods.

KEYWORDS:

• Hybrid Bernstein Block–Pulse functions
• system of fractional integro-differential equations
• convergence analysis
• numerical algorithm
• Gaussian quadrature

AMS CLASSIFICATIONS:

• 26A33
• 65L20
• 68U20
• 65C20

Disclosure statement

No potential conflict of interest was reported by the authors.