On the well posedness of a mathematical model for a singular nonlinear fractional pseudo-hyperbolic system with nonlocal boundary conditions and frictional damping

TL;DR

This paper investigates the mathematical well-posedness of a nonlinear fractional pseudo-hyperbolic system with nonlocal boundary conditions, establishing existence and uniqueness of solutions using Sobolev fractional spaces and iterative methods.

Contribution

It provides the first rigorous analysis of the well-posedness for a singular nonlinear fractional pseudo-hyperbolic system with nonlocal boundary conditions.

Findings

Proved existence and uniqueness of solutions for the linear fractional system.

Established well-posedness of the nonlinear fractional system.

Applied the results to models in elastic vibrations and unsteady flows.

Abstract

This paper is devoted to the study of the well-posedness of a singular nonlinear fractional pseudo-hyperbolic system. The fractional derivative is described in Caputo sense. The equations are supplemented by classical and nonlocal boundary conditions. Upon some a priori estimates and density arguments, we establish the existence and uniqueness of the strongly generalized solution for the associated linear fractional system in some Sobolev fractional spaces. On the basis of the obtained results for the linear fractional system, we apply an iterative process in order to establish the well-posedness of the nonlinear fractional system. This mathematical model of pseudo-hyperbolic systems arises mainly in the theory of longitudinal and lateral vibrations of elastic bars (beams), and in some special case it is propounded in unsteady helical flows between two infinite coaxial circular cylinders for some specific boundary conditions.