the hölder and minkowski inequalities utilizing a fractional operator involvement of pseudo-operator

A generalized integral operator of order $alpha$ of a real function $f$  including a parameter set $p$, namely $k_p^alpha f(t)$ has been introduced by o. p.  agrawal  (computers and mathematics with applications, 59 (2010) 1852--1864), which is a generalization of some important fractional integrals such as the riemann-liouville fractional integral. using pseudo-analysis, this paper introduces a pseudo-operator integral of order $alpha$ including a parameter set $p$  in a semiring $([a, b], oplus, odot)$, which is  a generalization of  $k_p^alpha f(t)$. we also discuss some particular cases and we obtain the well-known h{o}lder’s and minkowski’s  inequalities  for this kind of pseudo-operator integral. the results given in this paper provide a generalization of several inequalities obtained in earlier studies.