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The aim of this paper is to study the existence and uniqueness of solutions for nonlinear fractional relaxation integro-differential equations with boundary conditions. Some results about the existence and uniqueness of solutions have been established by using the Banach contraction mapping principle and the Schauder fixed point theorem. An example is provided which illustrates the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we consider a nonlinear neutral fractional difference equations. By applying Krasnoselskii's fixed point theorem, sufficient conditions for the existence of solutions are established. Also, the uniqueness of a solution is given. As an application of the main theorems, we provide the existence and uniqueness of the discrete fractional Lotka-Volterra model of neutral type. Our main results extend and generalize the results that are obtained in [6]. [ABSTRACT FROM AUTHOR]

Let T be a time scale such that 0, ti, T ∊ T, i = 1, 2, . . ., n, and 0 < ti < ti+1. Assume each ti is dense. Using a fixed point theorem due to Krasnoselskii-Burton, we show that the nonlinear impulsive dynamic equation ... where y(ti±) = lim t→t ± i y(t), and yΔ is the Δ-derivative on T, has a solution. [ABSTRACT FROM AUTHOR]

In this work we study a class of second order nonlinear delay integrodifferential equations x (t) + f (t, x (t), x (t)) x (t) + N/Σ/j=1 ftt-tj(t) a j (t, s) g j (s, x (s)) ds + N/Σ/j=1 b j (t) x' (t - Tj(t)) = 0, with variable delays and give some new conditions ensuring that the zero solution is asymptotically stable by means of the fixed point theory. Our work extends and improves previous results in the literature such as, D. Pi [17, 18] and T. A. Burton [10]. An example is given to illustrate our claim. [ABSTRACT FROM AUTHOR]

In this paper, we use a modification of Krasnoselskii's fixed point theorem introduced by Burton (see [8] Theorem 3) to obtain stability results of the zero solution of totally nonlinear neutral differential equations with functional delay x' (t) = -a (t) h (x (t - τ (t))) + c (t) x' (t - τ (t)) + G(t, x (t) , x (t - τ (t))) : The stability of the zero solution of this equation provided that h (0) = G(t; 0; 0) = 0. The Caratheodory condition is used for the function G. [ABSTRACT FROM AUTHOR]

In this paper, we study the asymptotic stability of a generalized nonlinear neutral differential equation with variable delays by using the fixed point theory. An asymptotic stability theorem with a necessary and sufficient condition is proved, which improves and generalizes some results due to Burton [11], Zhang [25], Dib, Maroun and Raffoul [16], and Ardjouni and Djoudi [3]. Two examples are also given to illustrate our results. [ABSTRACT FROM AUTHOR]