we prove the generalized hyers--ulam stability  of n--th order linear differential equation of the form $y^{(n)}+p_{1}(x)y^{(n-1)}+ cdots+p_{n-1}(x)y^{prime}+p_{n}(x)y=f(x)$, with condition that there exists a non--zero solution of corresponding homogeneous equation. our main results extend and improve the corresponding results obtained by many authors.

Abstract We consider in this paper modified fractional Korteweg–de Vries and related equations (modified Burgers–Hilbert Whitham). They have the advantage with respect to usual KdV equation a defocusing case different dynamics. will distinguish weakly dispersive where phase velocity is unbounded for low frequencies tends zero at infinity strongly vanishes origin goes infinity. In former case, n...

We consider the large time behavior of solutions to Cauchy problem for BBM-Burgers equation. prove that solution this goes self-similar Burgers equation called nonlinear diffusion wave. Moreover, we construct appropriate second asymptotic profiles depending on initial data. Based discussion, investigate effect data solution, and derive optimal rate Especially, important point study is with slow...

This paper address a new vision for the generalized Mittag-Leffler stability of the fractional differential equations. We mainly focus on a new method, consisting of decomposing a given fractional differential equation into a cascade of many sub-fractional differential equations. And we propose a procedure for analyzing the generalized Mittag-Leffler stability for the given fractional different...

The role of the renal apical brush-border membrane (BBM) endocytic receptors cubilin and megalin in the onset of albuminuria in rats exposed to a single dose of total body irradiation (TBI) has been investigated. Albuminuria was evident as immunoblot (IB) analysis of the urine samples from TBI rats revealed excretion of large amounts of albumin. IB analysis of the BBM proteins did not reveal an...

In previous studies we demonstrated that the biologically active vitamin D metabolite 1,25-dihydroxyvitamin D 11,25(OH)2D] increased the calmodulin (CaM) content of chick duodenal brush border membranes (BBM) without increasing the total cellular CaM content. Therefore, we evaluated the binding of CaM to discrete proteins in the BBM and determined whether 1,25(OH)2D could influence such binding...

The functional variable method is a powerful mathematical tool for obtaining exact solutions of nonlinear evolution equations in mathematical physics. In this paper, the functional variable method is used to establish exact solutions of the (2+1)-dimensional Kadomtsov-Petviashivilli-Benjamin-BonaMahony (KP-BBM) equation, the (2+1)-dimensional Konopelchenko-Dubrovsky equation, the (3+1)dimension...

BACKGROUND Surgical stress can lead to translocation of bacteria from the intestine into the systemic circulation. The intestinal brush border membrane (BBM) plays an important role in defense against such invasion by luminal bacteria and endotoxin. Our earlier work has shown the development of oxidative stress in the intestine after surgical stress and since the BBM is sensitive to free radica...

Somatic embryogenesis is an example of induced cellular totipotency, where embryos develop from vegetative cells rather than from gamete fusion. Somatic embryogenesis can be induced in vitro by exposing explants to growth regulators and/or stress treatments. The BABY BOOM (BBM) and LEAFY COTYLEDON1 (LEC1) and LEC2 transcription factors are key regulators of plant cell totipotency, as ectopic ov...

in this paper, we interpret a fuzzy differential equation by using the strongly generalized differentiability concept. utilizing the generalized characterization theorem. then a novel hybrid method based on learning algorithm of fuzzy neural network for the solution of differential equation with fuzzy initial value is presented. here neural network is considered as a part of large eld called n...