Conformable fractional Newton-type inequalities with respect to differentiable convex functions

Abstract

Abstract The authors propose a new method of investigation of an integral identity according to conformable fractional operators. Moreover, some Newton-type inequalities are considered for differentiable convex functions by taking the modulus of the newly established equality. In addition, we prove several Newton-type inequalities with the aid of Hölder and power-mean inequalities. Furthermore, several new results are given by using special choices of the obtained inequalities. Finally, we give several inequalities of conformable fractional Newton-type for functions of bounded variation.

Keywords

• Newton formula
• Fractional calculus
• Conformable fractional integrals