‎Semidiscrete finite element approximation of a hyperbolic type‎ ‎integro-differential equation is studied. The model problem is‎ ‎treated as the wave equation which is perturbed with a memory term.‎ ‎Stability estimates are obtained for a slightly more general problem.‎ ‎These, based on energy method, are used to prove optimal order‎ ‎a priori error estimates.‎

in this paper, some basic results concerning strict, nonstrict inequalities, local existence theorem and differential inequalities  have been proved for an ivp of first order hybrid  random differential equations with the linear perturbation of second type. a comparison theorem is proved and  applied to prove the uniqueness of random solution for the considered perturbed random differential equ...

Figure 1: Fundamental region R of the Modular Group, given by {z ∈ H : |z| > 1,− 2 ≤ Re(z) ≤ 1 2} The Klein Quartic curve is famous for its symmetries and many visualizations are created to capture these in lower dimensions. In fact, it has the largest possible automorphism group for its genus, the simple group of order 168. Yet, interest in this algebraic curve started with knowledge of the ex...

in this paper, we solve a inhomogeneous fractional klein-gordon equation by the method of separating variables. we apply the method for three boundary conditions, contain dirichlet, neumann, and robin boundary conditions, and solve some examples to illustrate the effectiveness of the method.

Solution of the nonlinear Klein-Gordon equation perturbed by small external force is investigated. The frequency of perturbation varies slowly and passes through a resonance. The resonance generates a solitary packets of waves. Full asymptotic description of this process is presented. Introduction This work is devoted to the problem on a generation of solitary packets of waves by a small extern...

In this paper, we consider a coupled system of nonlinear fractional differential equations (FDEs), such that both equations have a particular perturbed terms. Using emph{Leray-Schauder} fixed point theorem, we investigate the existence and multiplicity of positive solutions for this system.

Let complex matrices $A$ and $B$ have the same sizes. Using the singular value decomposition, we characterize the $g$-inverse $B^{(1)}$ of $B$ such that the distance between a given $g$-inverse of $A$ and the set of all $g$-inverses of the matrix $B$ reaches minimum under the unitarily invariant norm. With this result, we derive additive and multiplicative perturbation bounds of the nearest per...