@Article{cmes.2024.051588,
AUTHOR = {Iqbal M. Batiha, Rania Saadeh, Iqbal H. Jebril, Ahmad Qazza, Abeer A. Al-Nana, Shaher Momani},
TITLE = {Composite Fractional Trapezoidal Rule with Romberg Integration},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {140},
YEAR = {2024},
NUMBER = {3},
PAGES = {2729--2745},
URL = {http://www.techscience.com/CMES/v140n3/57261},
ISSN = {1526-1506},
ABSTRACT = {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.},
DOI = {10.32604/cmes.2024.051588}
}