Narrow Results

In this paper, we investigate a nonlocal multi-point and multi-strip coupled boundary value problem of nonlinear fractional Langevin equations. The standard fixed point theorems (Leray–Schauder’s alternative and Banach’s fixed point theorem) are applied to derive the existence and uniqueness results for the given problem. We also discuss the Ulam–Hyers stability for the given system. Examples illustrating the obtained results are presented. Some new results appearing as special cases of the present ones are also indicated.

In this paper, we deal with the existence and uniqueness (EU) of solutions for nonlinear Langevin fractional differential equations (FDE) having fractional derivative of different orders with nonlocal integral and anti-periodic-type boundary conditions. Also, we investigate the Hyres–Ulam (HU) stability of solutions. The existence result is derived by applying Krasnoselskii’s fixed point theorem and the uniqueness of result is established by applying Banach contraction mapping principle. An example is offered to ensure the validity of our obtained results.

We review the latest advances in the analytical modelling of single file diffusion. We focus first on the derivation of the fractional Langevin equation that describes the motion of a tagged file particle. We then propose an alternative derivation of the very same stochastic equation by starting from the diffusion-noise formalism for the time evolution of the file density.

 Special Issue Comments: This article presents mathematical formulations and results on the dynamics in files with applied potential, yet also general files. This article is connected to the Special Issue articles about the zig zag phenomenon,⁷² advanced statistical properties in single file dynamics,⁷³ and expanding files.⁷⁴