# A Numerical Calculation of Arbitrary Integrals of Functions

## DOI:

https://doi.org/10.21467/ajgr.7.1.11-17## Abstract

This paper presents a numerical technique for solving fractional integrals of functions by employing the trapezoidal rule in conjunction with the finite difference scheme. The proposed scheme is only a simple modification of the trapezoidal rule, in which it is treated as an algorithm in a sequence of small intervals for finding accurate approximate solutions to the corresponding problems. This method was applied to solve fractional integral of arbitrary order α > 0 for various values of alpha. The fractional integrals are described in the Riemann-Liouville sense. Figurative comparisons and error analysis between the exact value, two-point and three-point central difference formulae reveal that this modified method is active and convenient.

## Keywords:

Finite difference, Integrals functions, fractional calculus, fractional integral, modified trapezoidal rule, Riemann-Liouville### Downloads

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*Adv. J. Grad. Res.*, vol. 7, no. 1, pp. 11-17, Oct. 2019.

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