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In this paper we give a classification of endomorphisms and additive mappings of a prime ring satisfying certain algebraic identities. Moreover, we provide an example proving that the primeness hypothesis imposed in our theorems is not superfluous. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence and uniqueness of solutions for a tripled system of fractional differential equations with nonlocal integro multi point boundary conditions by using the p-Laplacian operator and the γ-Caputo derivatives. The presented results are obtained by the two fixed point theorems of Banach and Krasnoselskii. An illustrative example is presented at the end to show the applicability of the obtained results. To the best of our knowledge, this is the first time where such problem is considered. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence of solutions for fractional differential equations of arbitrary order with nonlocal integral boundary conditions. The existence results are obtained by applying Krasnoselskii's fixed point theorem and Leray-Schauder degree theory, while the uniqueness of the solutions is established by means of Banach's contraction mapping principle. The paper concludes with illustrative examples. [ABSTRACT FROM AUTHOR]

A graph G is called a fractional ID-k-factor-critical graph if after deleting any independent set of G the resulting graph admits a fractional k-factor. In this paper, we prove that for k≥2, G is a fractional ID-k-factor-critical graph if δ(G) ≥n/3+k,σ2(G)≥4n/3,n≥6k-8 The result is best possible in some sense. [ABSTRACT FROM AUTHOR]

In this paper, we study a coupled system of nonlinear fractional differential equations with multi-point boundary conditions. The differential operator is taken in the Riemann-Liouville sense. Applying the Schauder fixed-point theorem and the contraction mapping principle, two existence results are obtained for the following system {D0+αx(t) = f (t, y(t), D0+py(t)), t ∈ (0, 1), {D0+βy(t) = g (t, x(t), D0+qx(t)), t ∈ (0, 1), {x(0) = x'(0) = x''(0) = ⋯ = x(m-2)(0) = 0, x(1) = λx(ξ), {y(0) = y'(0) = y''(0) = ⋯ = y(m-2)(0) = 0, y(1) = λy(ξ), where 0 < ξ < 1, m ∈ N; m ≥ 2, α, β ∈ (m-1, m) and α, β, p, q, λ satisfy certain conditions. [ABSTRACT FROM AUTHOR]

Discussions are presented by Morita and Sato in Mathematics 2017; 5, 62: 1–24, on the problem of obtaining the particular solution of an inhomogeneous ordinary differential equation with polynomial coefficients in terms of the Green's function, in the framework of distribution theory. In the present paper, a compact recipe in nonstandard analysis is presented, which is applicable to an inhomogeneous ordinary and also fractional differential equation with polynomial coefficients. The recipe consists of three theorems, each of which provides the particular solution of a differential equation for an inhomogeneous term, satisfying one of three conditions. The detailed derivation of the applications of these theorems is given for a simple fractional differential equation and an ordinary differential equation. [ABSTRACT FROM AUTHOR]