In this paper, a vaccination model for SARS-CoV-2 variants is proposed and studied using fractional differential operators involving non-singular kernel. It worth mentioning that variability in transmission rates occurs because of the particular population vaccinated, hence, asymptomatic infected classes are classified on basis their history. Using Banach contraction principle Arzela–Ascoli the...

Summary . In this article we formalize the Ascoli-Arzelà theorem [5], [6], [8] in Mizar [1], [2]. First, gave definitions of equicontinuousness and equiboundedness a set continuous functions [12], [7], [3], [9]. Next, formalized using those definitions, proved theorem.

0 |f(s)|ds ≤ |t| ≤ 1. Therefore the image of Bp is (uniformly) bounded. By Arzela-Ascoli, V : L p[0, 1]→ C[0, 1] is compact. The preceeding argument does not go through when V acts on L1[0, 1]. In this case equicontinuity fails, as is demonstrated by the following family {fn} ⊂ B1: fn(s) = n1[0,1/n](s). This suffices to preclude compactness of V ; in particular, V fn has no Cauchy subsequence. ...

We generalize the Arzelà-Ascoli theorem to the setting of matrix order unit spaces, extending the work of Antonescu-Christensen on unital C∗algebras. This gives an affirmative answer to a question of Antonescu and Christensen.

An Arzelà-Ascoli theorem for asymmetric metric spaces (sometimes called quasi-metric spaces) is proved. One genuinely asymmetric condition is introduced, and it is shown that several classic statements fail in the asymmetric context if this assumption is dropped.

Ascoli theorems characterize “precompact” subsets of the set of morphisms between two objects of a category in terms of “equicontinuity” and “pointwise precompactness,” with appropriate definitions of precompactness and equicontinuity in the studied category. An Ascoli theorem is presented for sets of continuous functions from a sequential space to a uniform space. In our development we make ex...

In this paper, we discuss nonlinear fractional difference equations with the Caputo like difference operator. Some asymptotic stability results of equations under investigated are obtained by employing Schauder fixed point theorem and discrete Arzela-Ascoli’s theorem. Three examples are also provided to illustrate our main results.