Ulam stability and data dependence for fractional differential equations with Caputo derivative

In this paper, Ulam stability and data dependence for fractional differential equations with Caputo fractional derivative of order $\alpha$ are studied. We present four types of Ulam stability results for the fractional differential equation in the case of $0<\alpha<1$ and $b=+\infty$ by virtue of the Henry-Gronwall inequality. Meanwhile, we give an interesting data dependence results for the fractional differential equation in the case of $1<\alpha<2$ and $b<+\infty$ by virtue of a generalized Henry-Gronwall inequality with mixed integral term. Finally, examples are given to illustrate our theory results

Angiotensin II mediates the high-glucose-induced endothelial-to-mesenchymal transition in human aortic endothelial cells

<p>Abstract</p> <p>Background</p> <p>Substantial evidence suggests that high glucose (HG) causes endothelial cell damage; however, the potential mechanism therein has yet to be clarified. The aim of this study was to investigate the influence of HG on the endothelial-to-mesenchymal transition (EndMT) and its relevance to the activation of the renin-angiotensin system.</p> <p>Methods</p> <p>Primary human aortic endothelial cells (HAECs) were divided into three groups: a normal glucose (NG) group, HG group, and irbesartan (1 μM)-treated (HG+irbesartan) group. The concentration of angiotensin II in the supernatant was detected by radioimmunoassay. Pathological changes were investigated using fluorescence microscopy and electron microscopy. Immunofluorescence staining was performed to detect the co-expression of CD31 and fibroblast markers, such as fibroblast-specific protein 1 (FSP1). The expressions of FSP1 and α-SMA were detected by RT-PCR and Western blot.</p> <p>Results</p> <p>The treatment of HAECs in the HG group resulted in significant increases in the expressions of FSP1 and angiotensin II in dose-and time-dependent manners. The incubation of HAECs exposure to HG resulted in a fibroblast-like phenotype, wherein increased microfilamentation and a roughened endoplasmic reticulum structure were observed in the cytoplasm. The expressions of FSP1 and α-SMA were significantly increased in the HG group, and these changes were inhibited by irbesartan treatment (<it>P </it>< 0.05). Double staining of the HAECs indicated a co-localization of CD31 and FSP1 and that some cells acquired spindle-shaped morphologies and a loss of CD31 staining; however, treatment with irbesartan attenuated the expression of EndMT (<it>P </it>< 0.05).</p> <p>Conclusions</p> <p>These findings suggest a novel mechanism in HG-induced endothelial damage via the mediation of the EndMT by angiotensin II, which was inhibited by Irbesartan.</p

Existence and uniqueness results for fractional differential equations with boundary value condition

Tyt. z nagłówka.Bibliogr. s. 641-642.Dostępny również w formie drukowanej.ABSTRACT: In this paper, we study the existence and uniqueness of fractional differential equations with boundary value conditions. A new generalized singular type Gronwall inequality is given to obtain important a priori bounds. Existence and uniqueness results of solutions are established by virtue of fractional calculus and fixed point method under some weak conditions. An example is given to illustrate the results. KEYWORDS: fractional differential equations, boundary value conditions, singular gronwall inequality, existence, uniqueness

Existence and uniqueness results for fractional differential equations with boundary value conditions

In this paper, we study the existence and uniqueness of fractional differential equations with boundary value conditions. A new generalized singular type Gronwall inequality is given to obtain important a priori bounds. Existence and uniqueness results of solutions are established by virtue of fractional calculus and fixed point method under some weak conditions. An example is given to illustrate the results

Differential equations of fractional order alphain(2,3)alphain (2,3) with boundary value conditions in abstract Banach spaces

In this paper, we study boundary value problems for differential equations involving Caputo derivative of order $alphain (2,3)$ in Banach spaces. Some sufficient conditions for the existence and uniqueness of solutions are established by virtue of fractional calculus, a special singular type Gronwall inequality and fixed point method under some suitable conditions. Examples are given to illustrate the main results

Analysis of Walking Accessibility of Park Green Space in Weidu District of Xuchang City Based on GIS

Taking the park green space in Weidu District of Xuchang City as the research object, the spatial service area of the park green space under the mode of pedestrian transportation is analyzed by using the grid analysis function of geographic information system (GIS). The results show that under the walking mode in the research area, only less than 1/10 of the residents can walk to the park within 10 minutes, and nearly 1/5 of the residents can enjoy the service function of urban park green space within 20 minutes. Under the walking mode of 30 minutes, the accessibility area of park green space is only 36.63%, which is mainly concentrated in the new urban area. There are many urban parks with large scale. The number of urban parks in the old urban area is small and the accessibility is relatively poor. The research results can provide theoretical basis for optimizing the spatial structure of green space in Weidu District of Xuchang City

Grouting Process Simulation Based on 3D Fracture Network Considering Fluid–Structure Interaction

Grouting has always been the main engineering measure of ground improvement and foundation remediation of hydraulic structures. Due to complex geological conditions and the interactions between the grout and the fractured rock mass, which poses a serious challenge to the grouting diffusion mechanism analysis, fracture grouting has been a research hotspot for a long time. In order to throw light on the grout diffusion process in the fractured rock mass and the influence of grout on the fracture network, and to achieve more realistic grouting numerical simulation, in this paper a grouting process simulation approach considering fluid&ndash;structure interaction is developed based on the 3D fractured network model. Firstly, the relationship between fracture apertures and trace lengths is used to obtain a more realistic value of fracture aperture; then a more reliable model is established; subsequently, based on the 3D fracture network model, different numerical models are established to calculate fluid dynamics (grout) and structure deformation (fractured rock mass), and the results are exchanged at the fluid&ndash;structure interface to realize the grouting process simulation using two-way fluid-structure interaction method. Finally, the approach is applied to analyze the grouting performance of a hydropower station X, and the results show that the grouting simulation considering fluid&ndash;structure interaction are more realistic and can simultaneously reveal the diffusion of grout and the deformation of fracture, which indicates that it is necessary to consider the effect of fluid&ndash;structure interaction in grouting simulation. The results can provide more valuable information for grouting construction

Additional file 2: Table S1. of Appropriate NH4 +: NO3 − ratio improves low light tolerance of mini Chinese cabbage seedlings

The concentrations of salts (mmol L−1) used to prepare macronutrient solutions at NH4 +: NO3 − ratios of 0: 100, 10:90, 15:85 and 25:75. (DOCX 16 kb

Additional file 3: Table S2. of Appropriate NH4 +: NO3 − ratio improves low light tolerance of mini Chinese cabbage seedlings

Primer sequences, annealing temperature and Genebank accession number of the rbcL, rbcS, GAPDH, FBPase, FBA, TK and actin gene sequences. (DOCX 18 kb