In this article, we study the existence of mild solutions for nonlocal Cauchy problem for fractional neutral evolution equations with infinite delay. The results are obtained by using the Banach contraction principle. Finally, an application is given to illustrate the theory. Full text

The paper is concerned with the asymptotic behavior of solutions to a second order nonlinear differential equation u′′ + f (t, u) = 0. Using the Banach contraction principle, we establish global existence of solutions which satisfy u(t) = At + o(tν) as t→ +∞, where A ∈ R and ν ∈ (0, 1].

In this paper, by using the Schauder fixed point theorem and the Banach contraction principle, we investigate existence and uniqueness of solutions for a class of multi-point boundary value problems of nonlinear fractional q-difference equations. As applications, two examples are presented to show the effectiveness of the obtained results.

The solution to a sequential fractional differential equation with affine periodic boundary value conditions is investigated in this paper. existence theorem of established by means the Leray–Schauder fixed point and Krasnoselskii theorem. What more, uniqueness demonstrated via Banach contraction mapping principle. In order illustrate main results, two examples are listed.

The main purpose of this paper is to investigate the existence and Ulam-Hyers stability (U-Hs) solutions a nonlinear neutral stochastic fractional differential system. We prove uniqueness proposed system by using fixed point theorems Banach contraction principle. Also, fundamental schemes calculus, we study our suggested Besides, an example, best describing result.

We prove two new fixed point theorems for generalized metric spaces and show that various fundamental fixed point principles, including: Banach Contraction Principle, Caristi fixed point theorem for metric spaces, Knaster-Tarski fixed point theorem for complete lattices, and the Bourbaki-Witt fixed point theorem for directed-complete orders, follow as corollaries of our results.

A system of higher-order nonlinear fractional differential equations is studied in this article, and some sufficient conditions for existence and uniqueness of a solution for the system is established by the nonlinear alternative of Leray-Schauder and Banach contraction principle.

In this paper, we consider the second-order nonlinear and the nonlinear neutral functional differential equations (a(t)x′(t))′ + f(t, x(g(t))) = 0, t ≥ t0 (a(t)(x(t)− p(t)x(t− τ))′)′ + f(t, x(g(t))) = 0, t ≥ t0 . Using the Banach contraction mapping principle, we obtain the existence of throughout positive solutions for the above equations.