On an initial boundary value problem for fractional pseudo-parabolic equation with conformable derivative

Author:

Nguyen Huy Tuan12,Tien Nguyen Van345,Yang Chao67

Affiliation:

1. Division of Applied Mathematics, Science and Technology Advanced Institute, Van Lang University, Ho Chi Minh City, Vietnam

2. Faculty of Applied Technology, School of Engineering and Technology, Van Lang University, Ho Chi Minh City, Vietnam

3. Department of Mathematics and Computer Science, University of Science, Ho Chi Minh City, Vietnam

4. Vietnam National University, Ho Chi Minh City, Vietnam

5. Faculty of Math, FPT University HCM, Saigon Hi-Tech Park, Thu Duc City, Ho Chi Minh City, Vietnam

6. College of Mathematical Sciences, Harbin Engineering University, Harbin 150001, China

7. Faculty of Applied Mathematics, AGH University of Science and Technology, 30-059 Kraków, Poland

Abstract

<abstract><p>In this paper, we study the initial boundary value problem of the pseudo-parabolic equation with a conformable derivative. We focus on investigating the existence of the global solution and examining the derivative's regularity. In addition, we contributed two interesting results. Firstly, we proved the convergence of the mild solution of the pseudo-parabolic equation to the solution of the parabolic equation. Secondly, we examine the convergence of solution when the order of the derivative of the fractional operator approaches $ 1^- $. Our main techniques used in this paper are Banach fixed point theorem and Sobolev embedding. We also apply different techniques to evaluate the convergence of generalized integrals encountered.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Applied Mathematics,Computational Mathematics,General Agricultural and Biological Sciences,Modeling and Simulation,General Medicine

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