Also, it is possible to construct FAC by means of Erdeyi-Kober fractional integral for example or hyperdifferential non-local operators.
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.
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].
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.
During the past decades, with the development of the theory of differential and integral equations, a lot of integral inequalities, for example [1 12], have been discovered, which play an important role in the research of boundedness, global existence, stability of solutions of differential and integral equations.
This integral is now known as the 'Katugampola fractional integral' see for example [20], pp.15,123.
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].
As an important branch of the Gronwall-Bellman inequality, various weakly singular integral inequalities and their discrete analogues have attracted more and more attention and play a fundamental role in the study of the theory of singular differential equations and integral equations (for example, see [1 8] and [9]).
Furthermore, some author works to be approximate to Abel integral equations, for example, Garza in [12] and Hall in [13] used the wavelet method, Legendre wavelets approximation by Yousefi in [19], Gauss Jacobi quadrature rule by Fettis in [10], and Piessens and Verbaeten in [16, 17] with Chebyshev polynomials of the first kind.
