The purpose of this paper is to investigate the existence and uniqueness mild solutions a semilinear Cauchy problem for an abstract fractional differential equation with state dependent nonlocal condition. Continuous dependence on initial conditions local ????-approximate solution considered will be discussed.

In this paper, we study a class of impulsive neutral stochastic functional integro-differential equations with infinite delay driven by a standard cylindrical Wiener process and an independent cylindrical fractional Brownian motion (fBm) with Hurst parameter H 2 ð1=2; 1Þ in the Hilbert space. We prove the existence and uniqueness of the mild solution for this kind of equations with the coeffici...

In this study, a new mild steel surface pretreatment solution is introduced based on phosphoric acid containing a benzimidazole derivative as inhibitor. In this way, three different benzimidazole derivatives namely benzimidazole BI, 2-methyl benzimidazole 2MBI and 2-aminobenzimidazole 2ABI were studied in the 1M H3PO4 using DC and AC electrochemical techniques. Results revealed the better corro...

Corrosion behavior of mild steel in chloride contaminated alkaline solution has been studied for the period up to 100days. Saturated Calcium hydroxide solution was used as alkaline solution and 0.5M NaCl solution was used to accelerate mild steel corrosion. The Charge transfer resistance Rct, Current density Icorr and inhibition efficiency values were obtained from tafel polarization and electr...

*Correspondence: [email protected] School of Mathematics and Statistics, Chong Qing University, Chong Qing, P.R. China Abstract The existence and uniqueness of a mild solution to stochastic equations with jumps are established, a stochastic Fubini theorem and a type of Burkholder-Davis-Gundy inequality are proved, and the two formulas are used to study the regularity property of the mild sol...

This paper studies the existence and global asymptotical stability of periodic PC-mild solution for the T -periodic logistic system with time-varying generating operators and T0-periodic impulsive perturbations on Banach spaces. Two sufficient conditions that guarantee the exponential stability of the impulsive evolution operator corresponding to homogenous well-posed T -periodic system with ti...

We study the existence of mild solutions for semilinear fractional differential equations with nonlocal initial conditions in $L^p([0,1],E)$, where $E$ is a separable Banach space. The main ingredients used in the proof of our results are measure of noncompactness, Darbo and Schauder fixed point theorems. Finally, an application is proved to illustrate the results of this work. 

In this paper we study, via variational methods, the problem of scattering of time harmonic acoustic waves by an unbounded sound soft surface. The boundary ∂D is assumed to lie within a finite distance of a flat plane and the incident wave is that arising from an inhomogeneous term in the Helmholtz equation whose support lies within some finite distance of the boundary ∂D. Via analysis of an eq...