Remark 2.5 The results of this paper can be given for more general time-scale integrals, for example, Lebesgue time-scale integrals in [19] or even multiple Lebesgue time-scale integrals in [20].
Also, it is possible to construct FAC by means of Erdeyi-Kober fractional integral for example or hyperdifferential non-local operators.
Calculate the hyper-singular integral of Example 4.1 with (g(x)=x^{4}+1) and the exact value of this finite-part integral is bigl(I(g bigr) (t)=4t^{2}+2t+frac{4}{ 3} frac{t+1}{t(t-1)}+4t^{3}lnfrac{t+1}{t t-1
It is noted that the behavior of the modifier in Equation 5 depends not only on the detection location of P x,z) but also on the dimension parameters of the slits b and d because they are coupled in the argument of the Fresnel integral, for example, u 1 = 1 / π c z - d - b - x, and the plasmon phase term exp ik sp ⋅2d) is related with d too.
Whilst regular references were made to 'Craft' and 'Medicine' students during sessions, given this was integral, for example, to the approach to pairing students for collaborative drawing activity, great care was taken to avoid any sense of enforcing specific subject-defined identities.
The number of needed function evaluations depends on the cubature rule applied to compute the projection integrals, for example using a Gaussian cubature tensor product rule we need ( s + 1 ) n function evaluations per timestep of the time integration method.
The map gis compact integral operator ([22], Example 2, p. 277).
A lot of authors presently are working on inequalities involving fractional integral operators, for example the versions of Riemann-Liouville, Caputo, Hillfer, Canvati etc.
Many mathematicians applied fixed point methods to the existence of unique solutions to non-linear integral equations, for example, refer to [3, 4, 9, 13 16].
For example, integral constraints can be considered to control the glucose level in the whole time interval ([0, T]) and a cost benefit analysis can also be taken into account.
