TY  - EJOU
AU  - Batiha, Iqbal M. 
AU  - Saadeh, Rania 
AU  - Jebril, Iqbal H. 
AU  - Qazza, Ahmad 
AU  - Al-Nana, Abeer A. 
AU  - Momani, Shaher 

TI  - Composite Fractional Trapezoidal Rule with Romberg Integration
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2024
VL  - 140
IS  - 3
SN  - 1526-1506

AB  - The aim of this research is to demonstrate a novel scheme for approximating the Riemann-Liouville fractional integral operator. This would be achieved by first establishing a fractional-order version of the -point Trapezoidal rule and then by proposing another fractional-order version of the -composite Trapezoidal rule. In particular, the so-called divided-difference formula is typically employed to derive the -point Trapezoidal rule, which has accordingly been used to derive a more accurate fractional-order formula called the -composite Trapezoidal rule. Additionally, in order to increase the accuracy of the proposed approximations by reducing the true errors, we incorporate the so-called Romberg integration, which is an extrapolation formula of the Trapezoidal rule for integration, into our proposed approaches. Several numerical examples are provided and compared with a modern definition of the Riemann-Liouville fractional integral operator to illustrate the efficacy of our scheme.
KW  - Composite fractional Trapezoidal rule; Romberg integration

DO  - 10.32604/cmes.2024.051588