This paper studies a fractional boundary value problem of nonlinear differential equations of arbitrary orders. New existence and uniqueness results are established using Banach contraction principle. Other existence results are obtained using Schaefer and Krasnoselskii fixed point theorems. In order to clarify our results, some illustrative examples are also presented.

In this paper, the approximate controllability of fractional impulsive neutral stochastic differential equations with nonlocal conditions and infinite delay in Hilbert spaces is studied. By using the Krasnoselskii-Schaefer-type fixed point theorem and stochastic analysis theory, some sufficient conditions are given for the approximate controllability of the system. At the end, an example is giv...

Motivated by the study of matter waves in Bose-Einstein condensates and coupled nonlinear optical systems, we study a system of two coupled nonlinear Schrödinger equations with inhomogeneous parameters, including a linear coupling. For that system we prove the existence of two different kinds of homoclinic solutions to the origin describing solitary waves of physical relevance. We use a Krasnos...

Existence and stability of periodic solutions are studied for a system of delay differential equations with two delays, with periodic coefficients. It models the evolution of hematopoietic stem cells and mature neutrophil cells in chronic myelogenous leukemia under a periodic treatment that acts only on mature cells. Existence of a guiding function leads to the proof of the existence of a stric...

The existence of solutions of boundary value problems for finite difference equations were studied by many authors, one may see the text books 1, 2 , the papers 3–5 and the references therein. We present some representative ones, which are the motivations of this paper. In papers 3, 4 , using Krasnoselskii fixed point theorem and Leggett-Williams fixed point theorem, respectively, Karakostas st...

In this paper, we prove a fixed point theorem for the sum of a nonlinear contraction mapping and compact operator. The fixed point theorem obtained here resembles that of Krasnoselskii in which the mapping function is a combination of contraction and compact operators. It also takes the form of Schaefer’s fixed point theorem of continuation type. Criteria on periodicity and control in integral ...