Certain Bounds Related to Multi-Parameterized <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-Fractional Integral Inequalities and Their Applications

Abstract

A $k$ -fractional integral identity with multiple parameters is investigated. Based on this identity, some estimation-type results related to $k$ -fractional integral inequalities for the first-order differentiable functions are obtained. These results are then applied to the estimation of cumulative distribution function and some other special means.

Keywords

• Hadamard’s inequality
• m)-preinvex functions%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> generalized (α,<italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">m</italic>)-preinvex functions
• k-fractional integrals%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">k</italic>-fractional integrals