Computer Simulation and Iterative Algorithm for Approximate Solving of Initial Value Problem for Riemann-Liouville Fractional Delay Differential Equations

Abstract

The main aim of this paper is to suggest an algorithm for constructing two monotone sequences of mild lower and upper solutions which are convergent to the mild solution of the initial value problem for Riemann-Liouville fractional delay differential equation. The iterative scheme is based on a monotone iterative technique. The suggested scheme is computerized and applied to solve approximately the initial value problem for scalar nonlinear Riemann-Liouville fractional differential equations with a constant delay on a finite interval. The suggested and well-grounded algorithm is applied to a particular problem and the practical usefulness is illustrated.

Keywords

• Riemann-Liouville fractional differential equation
• delay
• lower and upper solutions
• monotone-iterative technique