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One unusual property of dynamic systems, whose state is characterized by a set of scalar dynamic variables satisfying a system of differential equations of a general form, is considered. This property is related to the behavior of equations…
In this paper, we reformulate certain nabla fractional difference equations which had been investigated by other researchers. The previous results seem to be incomplete. By using Contraction Mapping Theorem, we establish conditions under…
In this paper, the Painlev\'e property to fractional differential equations (FDEs) are extended and the existence and uniqueness theorems for both linear and nonlinear FDEs are established. The results contribute to the research of…
In this article, we consider inverse problems of determining a source term and a coefficient of a first-order partial differential equation and prove conditional stability estimates with minimum boundary observation data and relaxed…
In this paper, we establish some fixed point theorems in ordered partial metric spaces. An example is given to illustrate our obtained results.
In this article, utilizing the concept of w-distance, we prove the celebrated Banach's fixed point theorem in metric spaces equipped with an arbitrary binary relation. Necessarily our findings unveil another direction of relation-theoretic…
In this article, we consider the boundary-value problem of nonlinear fractional differential equation with p-Laplacian operator. By the properties of Green function and Schauder fixed point theorem, several existence and nonexistence…
We consider a new fractional impulsive differential hemivariational inequality which captures the required characteristics of both the hemivariational inequality and the fractional impulsive differential equation within the same framework.…
We present initially the motivation, definition and basic properties of differential equations with proportional delay. In the last Section we present open problems.
In this paper, we obtain some new results about weakly singular integral inequalities. These inequalities are used to discuss the global existence and uniqueness results for fractional differential equations of Riemann-Liouville type. Some…
We study completeness in partial differential varieties. We generalize many results from ordinary differential fields to the partial differential setting. In particular, we establish a valuative criterion for differential completeness and…
An inverse problem to identify unknown coefficients of a partial differential equation by a single interior measurement is considered. The equation considered in this paper is a strongly elliptic second order scalar equation which can have…
In this paper, we investigate the sufficient conditions for existence and uniqueness of solutions and {\delta}-Ulam-Hyers-Rassias stability of an impulsive fractional differential equation involving $\psi$-Hilfer fractional derivative.…
Using exhaustion method and finite differences a new method to solve system of partial differential equations and is presented. This method allows design algorithm to solve linear and nonlinear systems in irregular domains. Applying this…
In this paper, we investigate a class of nonlinear impulsive stochastic differential evolution equations with infinite delay in Banach space. Based on the Krasnoselskii's fixed point theorem, sufficient conditions of the existence of the…
A numerical explicit method to evaluates transient solutions of linear partial differential inhomogeneous equation with constant coefficients is proposed. A general form of the scheme for a specific linear inhomogeneous equation is shown.…
In this note we shall introduce a simple, effective numerical method for solving partial differential equations for scalar and vector-valued data defined on surfaces. Even though we shall follow the traditional way to approximate the…
We consider some reaction-diffusion equations describing systems with the nonlocal consumption of resources and the intraspecific competition. Sharp conditions on the coefficients are obtained to ensure the stability and instability of…
Piezoelectric appliances have become hugely important in the past century and computer simulations play an essential part in the modern design process thereof. While much work has been invested into the practical simulation of piezoelectric…
We consider a Hilfer fractional differential equation with nonlocal Erd\'{e}lyi-Kober fractional integral boundary conditions. The existence, uniqueness and Ulam-Hyers stability results are investigated by means of the Krasnoselskii's fixed…