This paper is devoted to studying the representation of measures non-generalized compactness, in particular, noncompactness, non-weak compactness and non-super weak etc., defined on Banach spaces its applications. With aid a three-time order-preserving embedding theorem, we show that for every space X, there exist function C(K) some compact Hausdorff K an affine mapping $$\mathbb{T}$$ from supe...

In this paper we establish some convergence results for Riemann-Liouville, Caputo, and Caputo-Fabrizio fractional operators when the order of differentiation approaches one. We consider errors given by $\left|\left| D^{1-\al}f -f'\right|\right|_p$ p=1 $p=\infty$ prove that both Caputo Fabrizio is a positive real r, 0<r<1. Finally, compare speed between obtaining they related Digamma function.

First derivatives with respect to the parameters of Whittaker function $\mathrm{W}_{\kappa ,\mu }\left( x\right) $ are calculated. Using confluent hypergeometric function, these derivarives can be expressed as infinite sums quotients digamma and gamma functions. Also, it is possible obtain parameter in terms integrals integrands containing elementary functions (products algebraic, exponential l...