Sentence examples for using the established integral from inspiring English sources

Some interesting Hermite-Hadamard type integral inequalities involving Hadamard fractional integrals are also presented by using the established integral identities.

She stated, "We established integral relationships with Kara and Scott.

The above Corollary 2.2 can be also found in [23] where it was established by using the generalized beta integral technique.

In [3] the authors developed fractional calculus for vector-valued functions using the weak Riemann integral and they established the existence of weak solutions for a class of fractional differential equations with fractional weak derivatives.

The purpose of this paper is to establish some improvements of Minkowski's inequality by using the delta integral, the nabla integral and the diamond-α integral on time scales.

We could, of course, do that using the convolution integral.

Moreover, in our work, we use the beta integral to establish transformations two and three times, and this is a generalization of Krattenthaler and Rao's method.

for using the fermionic -adic integral on.

Images were captured digitally using the integral LSM software.

The obtained data were analyzed using the "integral mode".

CDF were generated using the integral function in Prism.