In this article, we show that Laplace transform can be applied to fractional system. To this end, solutions of linear fractional-order equations are first derived by a direct method, without using Laplace transform. Then the solutions of fractional-order differential equations are estimated by employing Gronwall and Hölder inequalities. They are showed be to of exponential order, which are nece...

Background & Aims of the Study: p-Chloronitrobenzene is a benzoic compound that widely used in many chemical industrials. p-Chloronitrobenzene may be absorbed through the skin and is suspected to causing cancer. So, developing an easy method to remove of it from the environment is necessary. Equilibrium isotherms and adsorption kinetics of p-Chloronitrobenzene onto modified sil...

We study stability of subsonic phase boundary solutions in the Suliciu model for phase transitions under tri-linear structural relation. With the help of Laplace transform, the evolution of perturbation is described by a linear dynamical system, and explicit solution is obtained in terms of inverse Laplace transform. Stability is established through energy estimates. The relaxed system is also ...

In this paper, we analyze the convergence of the preconditioned GMRESmethod for the first order finite element discretizations of the Helmholtz equation in media with losses. We consider a Laplace preconditioner, an inexact Laplace preconditioner and a two-level preconditioner. Our analysis is based on bounding the field of values of the preconditioned system matrix in the complex plane. The an...

This note presents the explicit form of the Laplace transform of the state transition matrix in the case of a system matrix being a companion matrix. Starting from this special case, we show how to compute the Laplace transform of the state transition matrix for any system matrix.1

Diffusion processes capture information about the geometry of an object such as its curvature, symmetries and particular points. The evolution of the diffusion is governed by the Laplace-Beltrami operator which presides to the diffusion on the manifold. In this paper, we define a new discrete adaptive Laplacian for digital objects, generalizing the operator defined on meshes. We study its eigen...

The Laplace-Beltrami operator on a Riemannian manifold, its spectral theory and the relations between its first eigenvalue and the geometrical data of the manifold, such as curvatures, diameter, injectivity radius, volume, has been extensively studied in the recent mathematical literature. In the last few years, another operator, called p-Laplacian, arising from problems on Non-Newtonian Fluids...

Searching minimizers of functions on the convenient level set of the constrain function we obtain weak solutions of a non-homogenuous p-Laplace equation in border case without using the regularity results of linear elliptic equations .

according to a class of constrained‎ ‎minimization problems‎, ‎the schwartz symmetrization process and the‎ ‎compactness lemma of strauss‎, ‎we prove that there is a‎ ‎nontrivial ground state solution for a class of $p$-laplace‎ ‎equations without the ambrosetti-rabinowitz condition‎.