Abstract
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 concerned with a class of nonlinear fractional Langevin equations involving nonsingular Mittag–Leffler (ML) kernel. We first investigate the existence and uniqueness of the solution by employing some fixed-point theorems. Then, we apply direct analysis to obtain the Ulam–Hyers (UH) type stability. Finally, the theoretical analysis and numerical simulation of some interesting examples show that there is a great difference between the fractional Langevin equation and integer Langevin equation in describing the random motion of free particles.
Subject
Statistics and Probability,Statistical and Nonlinear Physics,Analysis
Cited by
23 articles.
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