On a two-dimensional fractional thermoelastic system with nonlocal constraints describing a fractional Kirchhoff plate

Said Mesloub,Faten Aldosari

doi:10.1186/s13662-020-03188-6

Abstract

We show herein the existence and uniqueness of solutions for coupled fractional order partial differential equations modeling a thermoelastic fractional Kirchhoff plate model associated with initial, Dirichlet, and nonlocal boundary conditions involving fractional Caputo derivative. Some efficient results of existence and uniqueness are obtained by employing the energy inequality method.

Highlights

1 Introduction The systems of differential equations of time fractional order have been studied by many authors, and several results have been obtained
It is important to mention that fractional nonlocal problems are much harder to deal with, and this is because of the nonlocal nature of the fractional derivative and the nonlocal nature of the boundary condition
It seems that the functional analysis method we apply in this paper is very efficient to solve some nonlocal fractional initial boundary value problems for single

Summary

Introduction

The systems of differential equations of time fractional order have been studied by many authors, and several results have been obtained. It seems that the functional analysis method we apply in this paper is very efficient to solve some nonlocal fractional initial boundary value problems for single Where 1, 2, 3 designate the trace operators and ∂tα+1M is the time fractional Caputo derivative of order 1 + α with α ∈ (0, 1) for the function M [14], and it is given by the formula

Results

Conclusion