当前位置: X-MOL 学术Math. Methods Appl. Sci. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
On time fractional pseudo-parabolic equations with non-local in time condition
Mathematical Methods in the Applied Sciences ( IF 2.9 ) Pub Date : 2021-01-17 , DOI: 10.1002/mma.7196
Nguyen Huu Can 1 , Devendra Kumar 2 , Tri Vo Viet 3 , Anh Tuan Nguyen 3
Affiliation  

The main objective of the paper is to study the non-local problem for a pseudo-parabolic equation with fractional time and space. The derivative of time is understood in the sense of the time derivative of the Caputo fraction of the order α, 0 < α < 1. The first result is an investigation of the existence and uniformity of the solution; the formula for mild solution and the regularity properties will be given. The proofs are based on a number of sophisticated techniques using the Sobolev embedding and also on the construction of the Mittag–Lefler operator. In the second part, we investigate the convergence of the mild solution for non-local problem to the solution of the local problem when two non-local parameters reach 0. Finally, we present some numerical examples to illustrate the proposed method.

中文翻译:

时间条件非局部的时间分式伪抛物线方程

本文的主要目的是研究分数时空伪抛物方程的非局部问题。时间的导数理解为α阶 Caputo 分数的时间导数,0 <  α < 1. 第一个结果是调查解决方案的存在性和均匀性;将给出温和溶液的公式和正则性。证明基于使用 Sobolev 嵌入的许多复杂技术,以及 Mittag–Lefler 算子的构造。在第二部分中,我们研究了当两个非局部参数达到 0 时,非局部问题的温和解对局部问题解的收敛性。最后,我们给出了一些数值例子来说明所提出的方法。
更新日期:2021-01-17
down
wechat
bug