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


  • Received: 01 June 2022 Revised: 22 July 2022 Accepted: 26 July 2022 Published: 05 August 2022
  • 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.

    Citation: Huy Tuan Nguyen, Nguyen Van Tien, Chao Yang. On an initial boundary value problem for fractional pseudo-parabolic equation with conformable derivative[J]. Mathematical Biosciences and Engineering, 2022, 19(11): 11232-11259. doi: 10.3934/mbe.2022524

    Related Papers:

  • 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.



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