In the present work, we investigate the existence of a mild solution of the fractional order differential equation with impulsive conditions in a Banach space. We establish the existence of a mild solution by using some fixed point theorems and resolvent operator theory. We present an example for showing the effectiveness of the main theory. Mathematics subject classification (2010): 34K37, 34K...

We prove local-in-time existence of a unique mild solution for the tornado-hurricane equations in a Hilbert space setting. The wellposedness is shown simultaneously in a halfspace, a layer, and a cylinder and for various types of boundary conditions which admit discontinuities at the edges of the cylinder. By an approach based on symmetric forms we first prove maximal regularity for a linearize...

In this paper, we establish the existence of local and global mild solution for an impulsive fractional integro-differential equation with state dependent delay subject to nonlocal initial condition. The existence results for local mild solution are proved by applying the Schauder, nonlinear Larey Schauder alternative and Banach fixed point theorems. Then, we prove global existence result. An e...

We outline the ability of zinc phosphate coatings, obtained by chemical conversion, to protect mild steel rebars against localized corrosion, generated by chloride ions in alkaline media. The corrosion resistance of coated steel, in comparison with uncoated rebars and coated and uncoated steel rebars embedded in mortar, were evaluated by open-circuit potential, potentiodynamic polarization, cro...

We consider the abstract initial value problem for evolution equations which describe heat convection of incompressible viscous isotropic fluids with the asymmetric stress tensor. It is difficulty in the law of conservation of energy that the dissipation function must be taken into account. This problem has uniquely a mild solution. Moreover, a mild solution of this problem can be a strong or c...