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This paper studies the existence of periodic solutions of a third order iterative differential equation. The main tool used here is Krasnoselskii-Burton’s fixed point theorem dealing with a sum of two mappings, one is a large contraction and the other is compact.

This paper provides sufficient conditions to guarantee the existence, uniqueness and continuous dependence of positive solutions of a nonlinear fourth order iterative differential equations with two-point and integral boundary conditions. The main arguments are based on the Schauder fixed point theorem to prove the existence of a positive solution. As an application, we given an example to illustrate the obtained results.

In this article we study the existence of positive solutions for second-order nonlinear neutral dynamic equations on time scales. The main tool employed here is Schauder’s fixed point theorem. The results obtained here extend the work of Culakova, Hanustiakova and Olach [12]. Two examples are also given to illustrate this work.

In this paper, we study the existence, uniqueness and estimate of solutions for nonlinear hybrid implicit Caputo fractional differential equations by using the contraction mapping principle and the generalization of Gronwall's inequality. After that, we also establish the Ulam stability for the problem at hand. Finally, an example is given to illustrate this work.

In this paper, the following third-order nonlinear delay differential equation with periodic coefficients x'''(t) + p(t)x''(t) + q(t)x'(t) + r(t)x(t) = f(t,x(t), x(t - t (t))) + d/dt g (t, x(t - t (t))), is considered. By employing Green's function and Krasnoselskii's fixed point theorem, we state and prove the existence of positive periodic solutions to the third-order nonlinear delay differential equation.

In this paper, we study the existence and uniqueness of solutions for time-fractional Oldroyd-B fluid equations with generalized fractional derivatives. We distinguish two cases. Firstly for the linear case, we get regularity results under some hypotheses of the source function and the initial data. Secondly for the nonlinear case, we use the Banach fixed point theorem to obtain the existence and uniqueness of solutions. [ABSTRACT FROM AUTHOR]

In this current manuscript, a class of neutral hyperbolic partial fractional functional differential equations (FPDEs) involving the generalized Caputo partial fractional derivative is investigated. The existence and uniqueness results are established based on some known tools of fixed point theory. In the end, two suitable examples are provided to demonstrate the obtained outcomes. [ABSTRACT FROM AUTHOR]

In this paper. we consider a one-dimensional Timoshenko system with a nonlinear damping term. First. we show the existence and uniqueness of the solution by using the semi-group method. more precisely by the Hille-Yosida theorem. Also. by constructing a suitable Lyapunov functional and using some properties of convex functions. we establish a general decay result for the solution of the system. Moreover. our result does not depend on any relation between the parameters of the system. [ABSTRACT FROM AUTHOR]

The nonlinear dumping transmission system is what well be studying in this article. First, by applying the Hille-Yosida theorem, we demonstrate the existence and uniqueness of the solution. Additionally, we demonstrate general stability estimations by utilizing some characteristics of convex functions and Lyaponov functional. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some new existence and uniqueness results for higher order fractional differential equations and inclusions with multi-strip Hadamard type fractional integral boundary conditions. In the case of inclusion problem, the existence results are established for convex as well as nonconvex multivalued maps. Our results are based on some fixed point theorems. Finally, an example is given to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of periodic and non-negative periodic solutions of the nonlinear neutral differential equation ddtx(t)=−a (t) h (x (t))+ddtQ (t, x (t−τ (t)))+G (t, x(t), x (t−τ (t))).$${{\rm{d}} \over {{\rm{dt}}}}{\rm{x}}({\rm{t}}) = - {\rm{a}}\;({\rm{t}})\;{\rm{h}}\;({\rm{x}}\;({\rm{t}})) + {{\rm{d}} \over {{\rm{dt}}}}{\rm{Q}}\;({\rm{t}},\;{\rm{x}}\;({\rm{t}} - {\rm \tau} \;({\rm{t}}))) + {\rm{G}}\;({\rm{t}},\;{\rm{x}}({\rm{t}}),\;{\rm{x}}\;({\rm{t}} - {\rm \tau} \;({\rm{t}}))).$$ We invert this equation to construct a sum of a completely continuous map and a large contraction which is suitable for applying the modificatition of Krasnoselskii’s theorem. The Caratheodory condition is used for the functions Q and G.

We use a variant of Krasnoselskii's fixed point theorem to show that the nonlinear difference equation with functional delay Δx (t) = - a (t) g (x (t)) + c (t)Δx(t_τ(t)) + q (t, x(t), x(t_τ(t))), has periodic solutions. For that end, we invert this equation to construct a fixed point mapping written as a sum of a completely continuous map and a large contraction which is suitable for the application of Krasnoselskii-Burton's theorem.

In the present paper we are going to consider in a one dimension bounded domain a transmission system with a varying delay. Under suitable assumptions on the weights of the damping and the delay terms, we prove the well-possedness and the uniqueness of solution using the semigroup theory. Also we show the exponential stability by introducing an appropriate Lyaponov functional.

In this paper, we study the existence and uniqueness of periodic solutions of the system of nonlinear neutral difference equations ∆x (n) = A(n) x (n - t (n)) + ∆Q(n; x (n - g (n))) + G(n; x (n) ; x (n - g (n))). By using Krasnoselski's fixed point theorem we obtain the existence of periodic solution and by contraction mapping principle we obtain the uniqueness. An example is given to illustrate our result. Our results extend and generalize the work [13].

In this paper we use the contraction mapping principle to obtain asymptotic stability results of a nonlinear neutral integro-differential equation with variable delay. An asymptotic stability theorem with a necessary and sufficient condition is proved, which improves and generalizes some previous results due to Burton [7], Becker and Burton [6] and Jin and Luo [17]. In the end we provide an example to illustrate our claim.