The Langevin system is an important mathematical model to describe Brownian motion. The
research shows that fractional differential equations have more advantages in …

The Langevin equation is a very important mathematical model in describing the random
motion of particles. The fractional Langevin equation is a powerful tool in complex …

In this paper, we consider fractional ordinary differential equations with not instantaneous
impulses. Firstly, we construct a uniform framework to derive a formula of solutions for …

Fractional Langevin system has great advantages in describing the random motion of
Brownian particles in complex viscous fluid. This manuscript deals with a delayed nonlinear …

In this paper, the concepts of Hyers–Ulam stability are generalized for non-autonomous
linear differential systems. We prove that the k-periodic linear differential matrix system Z˙(t) …

This paper proves the Hyers-Ulam stability and Hyers-Ulam-Rassias stability of first-order
non-linear delay differential equations with fractional integrable impulses. Our approach …

In this paper, we first utilize fractional calculus, the properties of classical and generalized
Mittag-Leffler functions to prove the Ulam–Hyers stability of linear fractional differential …

The fractional Langevin equation is a very effective mathematical model for depicting the
random motion of particles in complex viscous elastic liquids. This manuscript is mainly …

The theory of stability is an important branch of the qualitative theory of differential
equations. In 1940, Ulam [24] raised a problem when can we assert that the solutions of an …

The fractional Langevin equation has more advantages than its classical equation in
representing the random motion of Brownian particles in complex viscoelastic fluid. The …