In this paper, the Pfaff equations with continuous coefficients are considered. Analogs of Peanos existence theorem and Kamkes on uniqueness solution to Cauchy problem established, a method for approximate equation is proposed.

The main objective of this research manuscript is to establish various existence and uniqueness results as well the Ulam--Hyers stability solutions a Coupled system $\psi$--Caputo fractional differential equations without with delay in generalized Banach spaces. Existence are obtained by applying Krasnoselskii's type fixed point theorem, Schauder's theorem spaces, Perov's combined Bielecki norm...

Abstract In this study, an initial-value problem for a nonlinear Volterra functional integro-differential equation on finite interval was considered. The term in the contains multiple time delays. addition to giving some new theorems existence and uniqueness of solutions equation, authors also prove Hyers-Ulam-Rassias stability Hyers-Ulam equation. proofs use several different tools including B...

Abstract: This paper is devoted to studying the existence and uniqueness of weak solutions for an initial boundary problem of a nonlinear fourth-order parabolic equation with variable exponent vt + div(|∇4v|p(x)−2∇4v) − |4v|q(x)−24v = g(x, v). By applying Leray-Schauder’s fixed point theorem, the existence of weak solutions of the elliptic problem is given. Furthermore, the semi-discrete method...

Considering the second boundary value problem of Lagrangian mean curvature equation, we obtain existence and uniqueness smooth uniformly convex solution, which generalizes Brendle–Warren’s theorem about minimal diffeomorphism in Euclidean metric space.

In this paper we discuss the solvability of Langevin equations with two Hadamard fractional derivatives. The method discussion is to study solutions equivalent Volterra integral equation in terms Mittag–Leffler functions. existence and uniqueness results are established by using Schauder's fixed point theorem Banach's theorem, respectively. An example given illustrate main results.

We prove a general existence and uniqueness result of solutions for backward stochastic differential equation (BSDE) with Lipschitz condition. also establish continuous dependence property comparison theorem to this type BSDEs, thus strengthening existing results.

Abstract This article deals with the existence, uniqueness and Ulam-Hyers--Rassias stability results for a class of coupled systems implicit fractional differential equations Riesz-Caputo derivative boundary conditions. We will employ Banach’s contraction principle as well Schauder’s fixed point theorem to demonstrate our existence results. provide an example illustrate obtained