New error bounds for Newton’s formula associated with tempered fractional integrals

Abstract

Abstract In this paper, we first construct an integral identity associated with tempered fractional operators. By using this identity, we have found the error bounds for Simpson’s second formula, namely Newton–Cotes quadrature formula for differentiable convex functions in the framework of tempered fractional integrals and classical calculus. Furthermore, it is also shown that the newly established inequalities are the extension of comparable inequalities inside the literature.

Keywords

• Newton-type inequalities
• Quadrature formulae
• Fractional integrals
• Tempered fractional integrals