This paper describes a polynomial decay rate of the solution of the Kirchhoff type in viscoelasticity with logarithmic nonlinearity, where an asymptotically-stable result of the global solution is obtained taking into account that the kernel is not necessarily decreasing.

In this research article, we introduce a new class of hybrid Langevin equation involving two distinct fractional order derivatives in the Caputo sense and Riemann–Liouville fractional integral. Supported by three-point boundary conditions, we discuss the existence of a solution to this boundary value problem. Because of the important role of the measure of noncompactness in fixed point theory, we use the technique of measure of noncompactness as an essential tool in order to get the existence result. The modern analysis technique is used by applying a generalized version of Darbo’s fixed point theorem. A numerical example is presented to clarify our outcomes.

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is research paper is about the existence and uniqueness of the coupled system of nonlinear fractional Langevin equations with multipoint and nonlocal integral boundary conditions. e Caputo fractional derivative is used to formulate the fractional differential equations, and the fractional integrals mentioned in the boundary conditions are due to Atangana-Baleanu and Katugampola. e existence of solution has been proven by two main fixed-point theorems: O'Regan's fixed-point theorem and Krasnoselskii's fixed-point theorem. By applying Banach's fixed-point theorem, we proved the uniqueness result for the concerned problem. is research paper highlights the examples related with theorems that have already been proven. HindawiMathematical Problems in Engineering Volume 2020, Article ID 7345658, 15 pages https://doi.org/10.1155/2020/7345658