osp ( 1 | 2 ) -trivial deformation of osp ( 2 | 2 ) -modules structure on the spaces of symbols S d 2 of differential operators acting on the space of weighted densities F d 2 .

Let osp ( 2 | 2 ) be the orthosymplectic Lie superalgebra and osp ( 1 | 2 ) a Lie subalgebra of osp ( 2 | 2 ) . In our paper, we describe the cup-product H 1 ∨ H 1 , where H 1 : = H 1 ( osp ( 2 | 2 ) , osp ( 1 | 2 ) ; D λ , µ 2 ) is the first differential osp ( 1 | 2 ) -relative cohomology of osp ( 2 | 2 ) with coefficients in D λ , µ 2 and D λ , µ 2 : = Ho m diff ( F λ 2 , F µ 2 ) is the space of linear differential operators acting on weighted densities. This result allows us to classify the osp ( 1 | 2 ) -trivial deformations of the osp ( 2 | 2 ) -module structure on the spaces of symbols S d 2 . More precisely, we compute the necessary and sufficient integrability conditions of a given infinitesimal deformation of this action. Furthermore, we prove that any formal osp ( 1 | 2 ) -trivial deformations of osp ( 2 | 2 ) -modules of symbols is equivalent to its infinitisemal part. This work is the simplest generalization of a result by Laraiedh [17].

A novel HIV model through fractional enlarged integral and differential operators.

This article presents a novel mathematical fractional model to examine the transmission of HIV. The new HIV model is built using recently fractional enlarged differential and integral operators. The existence and uniqueness findings for the suggested fractional HIV model are investigated using Leray-Schauder nonlinear alternative (LSNA) and Banach's fixed point (BFP) theorems. Furthermore, multiple types of Ulam stability (U-S) are created for the fractional model of HIV. It is straightforward to identify that the gained findings may be decreased to many results obtained in former works of literature.