Related papers: Properties of Certain Partial dynamic Integrodiffe…
The objective of this work is to prove, in a first step, the existence and the uniqueness of a solution of the following multivalued deterministic differential equation: $dx(t)+\partial ^-\varphi (x(t))(dt)\ni dm(t),\ t>0$, $x(0)=x_0$,…
A semi-classical approach to the study of the evolution of anyonic excitations--elementary particles with fractional statistics, complementing bosons and fermions--is through the Boltzmann equation for anyons. This work reviews a…
We consider a singular fractional differential equation involving generalized Katugampola derivative and obtain the existence and uniqueness of its solution. A scheme for uniformly approximating solution is constructed by using Picard…
A nonlinear inequality is formulated in the paper. An estimate of the rate of decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations. It can be…
In this paper we make a study of a partial integral differential equation with $p$-Laplacian using a mixed finite element method. Two stable and convergent fixed point schemes are proposed to solve the nonlinear algebraic system. Using the…
Motivated by applications in data science, we study partial differential equations on graphs. By a classical fixed-point argument, we show existence and uniqueness of solutions to a class of nonlocal continuity equations on graphs. We…
The famous Banach Contraction Principle holds in complete metric spaces, but completeness is not a necessary condition -- there are incomplete metric spaces on which every contraction has a fixed point. The aim of this paper is to present…
We present new criteria on the existence of fixed points that combine some monotonicity assumptions with the classical fixed point index theory. As an illustrative application, we use our theoretical results to prove the existence of…
In this Note, we present a Calder\'on-type uniqueness theorem on the Cauchy problem of stochastic partial differential equations. To this aim, we introduce the concept of stochastic pseudo-differential operators, and establish their…
This paper recalls some classical motivations in fluid dynamics leading to a partial differential equation which is prescribed on a domain whose boundary possesses two connected components, one endowed with a Dirichlet datum, and the other…
In this article we present some integrability conditions for partial difference equations obtained using the formal symmetries approach. We apply them to find integrable partial difference equations contained in a class of equations…
This paper concerns with a mathematical modelling of biological experiments, and its influence on our lives. Fractional hybrid iterative differential equations are equations that interested in mathematical model of biology. Our technique is…
The well-posedness of a system of partial differential equations and dynamic boundary conditions, both of Cahn-Hilliard type, is discussed. The existence of a weak solution and its continuous dependence on the data are proved using a…
In this paper, sufficient conditions are established for the existence results of fractional order semilinear Volterra integrodifferential equations in Banach spaces. The results are obtained by using the theory of fractional cosine…
Random invariant manifolds are geometric objects useful for understanding complex dynamics under stochastic influences. Under a nonuniform hyperbolicity or a nonuniform exponential dichotomy condition, the existence of random pseudo-stable…
We study a class of quasi-variational inequality problems defined over infinite dimensional Banach space and deduce sufficient conditions for ensuring solutions to such problems under the upper semi-continuity and pseudomonotonicity…
We identify the stochastic processes associated with one-sided fractional partial differential equations on a bounded domain with various boundary conditions. This is essential for modelling using spatial fractional derivatives. We show…
The purpose of this paper is to present a universal approach to the study of controllability/observability problems for infinite dimensional systems governed by some stochastic/deterministic partial differential equations. The crucial…
We address the existence in the sense of sequences of solutions for a certain integro-differential type problem involving the logarithmic Laplacian. The argument is based on the fixed point technique when such equation contains the operator…
The integrability (solvability via an associated single-valued linear problem) of a differential equation is closely related to the singularity structure of its solutions. In particular, there is strong evidence that all integrable…