In this paper we develop the existence theory for a nonlinear Langevin equation involving Caputo fractional derivatives of different orders and Riemann-Liouville fractional integral supplemented with nonlocal multi-point and multi-strip boundary conditions. We make use of the modern methods of functional analysis to obtain the existence and uniqueness results for the given problem, which are well illustrated with the aid of examples. Our results are new and correspond to some new ones for specific choices of the parameters involved in the problem. Publisher's NoteSpringer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

In this paper, we investigate a new class of boundary value problems involving fractionaldifferential equations with mixed nonlinearities, and nonlocal multi-point and Riemann–Stieltjesintegral-multi-strip boundary conditions. Based on the standard tools of the fixed point theory,we obtain some existence and uniqueness results for the problem at hand, which are well illustratedwith the aid of examples. Our results are not only in the given configuration but also yield severalnew results as special cases. Some variants of the given problem are also discussed.

This paper is concerned with the oscillation of solutions of a class of third order nonlinear neutral differential equations. New sufficient conditions guarantee that every solution is either oscillatory or tends to zero are given. The obtained results improve some recent published results in the literature. Some illustrative examples are given.

In this paper, we study a new boundary value problem of arbitrary order fractional differential equations equipped with new integro-multipoint boundary conditions. Existence and uniqueness results for the given problem are obtained by applying the standard tools of fixed point theory. We also extend the problem at hand to its inclusions case and prove an existence result for it by applying a fixed point theorem due to Bohnenblust and Karlin.