Neutral Partial Differential Equations Research Articles

Asymptotic behavior of neutral partial differential equation under the light of semi‐Fredholm perturbation

Through this work, we establish the periodicity of solutions for the following neutral differential equation defined as . Applying the theory of perturbation of semi‐Fredholm operators, we purpose an a priori estimate on the bounded operator to derive the periodicity of bounded solutions on without taking of consideration the compactness of the semigroup generated by the part of . Moreover, we introduce an application includes numerical simulations to depict the applicability of theoretical findings.

Interpolating Stabilized Element Free Galerkin Method for Neutral Delay Fractional Damped Diffusion-Wave Equation

A numerical solution for neutral delay fractional order partial differential equations involving the Caputo fractional derivative is constructed. In line with this goal, the drift term and the time Caputo fractional derivative are discretized by a finite difference approximation. The energy method is used to investigate the rate of convergence and unconditional stability of the temporal discretization. The interpolation of moving Kriging technique is then used to approximate the space derivative, yielding a meshless numerical formulation. We conclude with some numerical experiments that validate the theoretical findings.

Some new oscillation results for third-order Emden-Fowler type neutral partial differential equations with mixed nonlinearities

Some new oscillation results for third-order Emden-Fowler type neutral partial differential equations with mixed nonlinearities

Traveling waves solutions for partial neutral differential equations

Using monotonicity techniques and the Schauder fixed point theorem, we study the existence of traveling waves for neutral partial differential equations. In the last section, we illustrate our results on the neutral versions of the KPP-Fisher and the Kobayashi equations.

English

English

Existence of mild solutions to partial neutral differential equations with non-instantaneous impulses

Existence of mild solutions to partial neutral differential equations with non-instantaneous impulses

Vibrational interpretation of a class of second order neutral partial differential equations

Vibrational interpretation of a class of second order neutral partial differential equations

Solutions to neutral partial functional differential equations with functional delay

An approximate solution to a neutral partial functional differential equation with functional delay is established by using method of semidiscretization. Sufficient conditions for the existence and uniqueness of a strong solution are also obtained.

Asymptotic behavior of solutions of impulsive neutral nonlinear partial differential equations with distributed delay

In this paper, the problem of asymptotic behavior of solutions for impulsive neutral partial differential equations has been investigated. Using Riccati transform method and impulsive differential inequalities, some new sufficient conditions are derived for a solution of the proposed equation which converges to zero. Finally, the effectiveness of the derived main results has been shown in numerical section.

On multiplicity of solutions to nonlinear partial difference equations with delay

In this paper, we present an existence criterion for multiple positive solutions of nonlinear neutral delay partial difference equations. Such equations can be regarded as a discrete analog of neutral delay partial differential equations. Our main result relies on fixed point index theory. An example is constructed to show the applicability of the obtained result.

Existence and uniqueness results for mild solutions of random impulsive abstract neutral partial differential equation over real axis

In this paper, we discuss the existence and uniqueness of mild solutions of random impulsive abstract neutral partial differential equations in a real separable Hilbert space. The results are obtained by using Leray-Schauder Alternative and Banach Contraction Principle. Finally an example is given to illustrate our problem.

Existence and Uniqueness of Solutions for Abstract Neutral Differential Equations with State-Dependent Delay

We study the existence and uniqueness of mild and strict solutions for abstract neutral differential equations with state-dependent delay. Some examples related to partial neutral differential equations are presented.

About global solution of nonhomogeneous neutral partial differential equation with deviating argument in the time variable

About global solution of nonhomogeneous neutral partial differential equation with deviating argument in the time variable

Traveling wave front for partial neutral differential equations

Traveling wave front for partial neutral differential equations

Oscillation of Even Order Impulsive Neutral Partial Differential Equations with Distributed Deviating Arguments

In this paper, we will consider a class of boundary value problems associated with even order nonlinear impulsive neutral partial functional differential equations with continuous distributed deviating arguments. Sufficient conditions are obtained for the oscillation of solutions using impulsive differential inequalities and integral averaging scheme with pair of boundary conditions. Examples are specified to point up our important results.

On The Oscillation of Impulsive Neutral Partial Differential Equations with Distributed Deviating Arguments and Damping Term

In this paper, we establish the Hyers-Ulam stability of the following Orthogonally Additive-Quadratic functional equation in Multi-Banach Spaces.ζ(2i + j) − ζ(i + 2j) − ζ(i + j) − ζ(j − i) − ζ(i) + ζ(j) + ζ(2j) = 0 with i⊥j where, ⊥ is orthogonality in the sense of Ratz.

On the Oscillation of Higher Order Impulsive Neutral Partial Differential Equations with Distributed Deviating Arguments

On the Oscillation of Higher Order Impulsive Neutral Partial Differential Equations with Distributed Deviating Arguments

Existence and Stability for Stochastic Impulsive Neutral Partial Differential Equations Driven by Rosenblatt Process with Delay and Poisson Jumps

Existence and Stability for Stochastic Impulsive Neutral Partial Differential Equations Driven by Rosenblatt Process with Delay and Poisson Jumps

On abstract degenerate neutral differential equations

We introduce a new abstract model of functional differential equations, which we call abstract degenerate neutral differential equations, and we study the existence of strict solutions. The class of problems and the technical approach introduced in this paper allow us to generalize and extend recent results on abstract neutral differential equations. Some examples on nonlinear partial neutral differential equations are presented.

Existence of solution and approximate controllability of a second-order neutral stochastic differential equation with state dependent delay

This paper has two sections which deals with a second order stochastic neutral partial differential equation with state dependent delay. In the first section the existence and uniqueness of mild solution is obtained by use of measure of non-compactness. In the second section the conditions for approximate controllability are investigated for the distributed second order neutral stochastic differential system with respect to the approximate controllability of the corresponding linear system in a Hilbert space. Our method is an extension of co-author N. Sukavanam's novel approach in [22]. Thereby, we remove the need to assume the invertibility of a controllability operator used by authors in [5], which fails to exist in infinite dimensional spaces if the associated semigroup is compact. Our approach also removes the need to check the invertibility of the controllability Gramian operator and associated limit condition used by the authors in [20], which are practically difficult to verify and apply. An example is provided to illustrate the presented theory.