This paper is concerned with the existence and uniqueness of mild solution of the fractional differential equations with nonlocal conditions d q xt/dt q −Axt ft, xt, Gxt, t ∈ 0, T, and x0 gx x 0 , in a Banach space X, where 0 < q < 1. General existence and uniqueness theorem, which extends many previous results, are given.

We study the existence and uniqueness of a mild solution to nonlinear Fokker-Planck equation with reflecting boundary conditions, by using monotonicity approach. Then we prove that is also distributional one.

In this article to prove existence of solution of infinite system of nonlinear integral equations, we consider the space of solution containing all convergence sequences with a finite limit, as with a suitable norm is a Banach space. By creating a generalization of Meir-Keeler condensing operators which is named as F-generalized Meir-Keeler condensing operators and measure of noncompactness, we...

We prove the (local) existence of a unique mild solution to a nonlinear moving-boundary problem of a mixed hyperbolic-degenerate parabolic type arising in modeling blood flow through compliant (viscoelastic) arteries.

In this work, we consider an impulsive non-autonomous semilinear equation with iterated deviating arguments in a Banach space. We establish the existence and uniqueness of a mild solution. Also we present an example that illustrates our main result.

In this paper, we introduce the logistic effect into the two-sex population model introduced by Hoppensteadt. We address the problem of existence and uniqueness of continuous and classical solutions. We first give sufficient conditions for a unique continuous solution to exist locally and also globally. Next, the existence of classical solutions is established under some mild assumptions on the...

We give two hypotheses of the relativistic collision kernal and show the existence and uniqueness of the global mild solution to the relativistic Enskog equation with the initial data near the vacuum for a hard sphere gas.