The n-Point Composite Fractional Formula for Approximating Riemann–Liouville Integrator

Abstract

In this paper, we aim to present a novel n-point composite fractional formula for approximating a Riemann–Liouville fractional integral operator. With the use of the definite fractional integral’s definition coupled with the generalized Taylor’s formula, a novel three-point central fractional formula is established for approximating a Riemann–Liouville fractional integrator. Such a new formula, which emerges clearly from the symmetrical aspects of the proposed numerical approach, is then further extended to formulate an n-point composite fractional formula for approximating the same operator. Several numerical examples are introduced to validate our findings.

Numerical Solution for Fractional-Order Mathematical Model of Immune-Chemotherapeutic Treatment for Breast Cancer Using Modified Fractional Formula

“…Based on these simulations it can be determined that the fractionalorder version of the differential system of the ICT carried out by the two numerical methods (FEM and MFEM) are completely considered. For more about fractional calculus and its applications, the reader may refer to [6,8,10,13,14].…”

“…The objective of this paper is to develop a numerical solution for the fractional-order differential system associated with ICT. We will employ a numerical scheme, the Modified Fractional Euler Method (MFEM), to solve this system and obtain numerical results see [2,6,8,10]. Anyhow, the ICT model can be described in the following manner:…”