Bounds for the Error in Approximating a Fractional Integral by Simpson’s Rule
Hüseyin Budak, Fatih Hezenci, Hasan Kara, Mehmet Zeki Sarıkaya
Abstract
Simpson’s rule is a numerical method used for approximating the definite integral of a function. In this paper, by utilizing mappings whose second derivatives are bounded, we acquire the upper and lower bounds for the Simpson-type inequalities by means of Riemann–Liouville fractional integral operators. We also study special cases of our main results. Furthermore, we give some examples with graphs to illustrate the main results. This study on fractional Simpson’s inequalities is the first paper in the literature as a method.
Topics & Concepts
MathematicsBounded functionFractional calculusType (biology)Applied mathematicsFunction (biology)Upper and lower boundsPure mathematicsMathematical analysisCalculus (dental)DentistryEvolutionary biologyMedicineEcologyBiologyMathematical Inequalities and ApplicationsMathematical functions and polynomialsApproximation Theory and Sequence Spaces