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This paper studies existence and uniqueness of solutions to generalized Volterra integral equations. Since our proof for existence and uniqueness does not make use of Banach fixed point theorem unlike the previous papers focused on this…
Stochastic diffusion equations are crucial for modeling a range of physical phenomena influenced by uncertainties. We introduce the generalized finite difference method for solving these equations. Then, we examine its consistency,…
The existence and uniqueness in fractional Sobolev spaces of the Cauchy problem to a stochastic parabolic integro-differential equation is investigated. A model problem with coefficients independent of space variable is considered. The…
In this paper, we investigate the existence and uniqueness of mild and strong solutions of fractional semilinear evolution equations in the Hilfer sense, by means of Banach fixed point theorem and the Gronwall inequality.
In this paper, we are interested in the study of a problem with fractional derivatives having boundary conditions of integral types. The problem represents a Caputo type advection-diffusion equation where the fractional order derivative…
This paper considers some the existence and uniqueness of strong solutions of stochastic neutral functional differential equations. The conditions on the neutral functional relax those commonly used to establish the existence and uniqueness…
A branch of generalizations of the Banach Fixed Point Theorem replaces contractivity by a weaker but still effective property. The aim of the present note is to extend the contraction principle in this spirit for such complete semimetric…
The overarching goal of this paper is to introduce and investigate a new nonlinear system driven by a nonlinear differential equation, a history-dependent quasivariational inequality, and a parabolic variational inequality in Banach spaces.…
We propose a method to obtain iterative schemes guarantee unique solutions for systems of partial differential equations that are not symmetric with respect to the time by generalizing He variational iteration method and using Banach fixed…
This monograph, written for educational purposes, serves as an introduction to the concept of integrability as it applies to systems of differential equations (both ordinary and partial) as well as to vector-valued fields. The general cases…
Our aim in this paper is to establish some strong stability properties of a solution of a stochastic differential equation driven by a fractional Brownian motion for which the pathwise uniqueness holds. The results are obtained using…
We present a theoretical framework and numerical methods for predicting the large-scale properties of solutions of partial differential equations that are too complex to be properly resolved. We assume that prior statistical information…
In this paper, we study a new type of stochastic functional differential equations which is called hybrid pantograph stochastic functional differential equations. We investigate several moment properties and sample properties of the…
This article addresses control problems for semilinear impulsive neutral integro-differential equations with memory in a Banach space. It investigates the approximate controllability of linear and semilinear systems and proves the…
In the paper a two-dimensional integro-differential system is considered. Using some variational methods we give sufficient conditions for the existence and uniqueness of a solution to the considered system. Moreover, we show that the…
In this paper, we obtained the sufficient conditions for the existence of solutions to the discrete boundary value problems of fractional difference equation depending on parameters. We use Krasnoselskii fixed point theorem to establish the…
Partial differential equations (PDEs) are at the heart of many mathematical and scientific advances. While great progress has been made on the theory of PDEs of standard types during the last eight decades, the analysis of nonlinear PDEs of…
In this paper, we investigate the existence and uniqueness of solutions for a fractional boundary value problem supplemented with nonlocal Riemann-Liouville fractional integral and Caputo fractional derivative boundary conditions. Our…
In this article, we consider a system of integro-differential equations in L^2(R, R^N), which contains the logarithmic Laplacian in the presence of transport terms. The linear operators associated with the system satisfy the Fredholm…
We study existence and uniqueness of bounded solutions to a fractional nonlinear porous medium equation with a variable density, in one space dimension.