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New Results On Continuity By Order Of Derivative For Conformable Parabolic Equations

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  • NGUYEN HUY TUAN

    (Division of Applied Mathematics, Science and Technology Advanced Institute, Van Lang University, Ho Chi Minh City, Vietnam2Faculty of Applied Technology, School of Engineering, Van Lang University, Ho Chi Minh City, Vietnam)

  • VAN TIEN NGUYEN

    (Faculty of Mathematics and Computer Science, University of Science, Ho Chi Minh City, Vietnam4Vietnam National University, Ho Chi Minh City, Vietnam5Department of Mathematics, FPT University, Hanoi, Vietnam)

  • DONAL O’REGAN

    (School of Mathematical and Statistical Sciences, National University of Ireland, Galway, Ireland)

  • NGUYEN HUU CAN

    (Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam)

  • VAN THINH NGUYEN

    (Department of Civil and Environmental Engineering, Seoul National University, Seoul, South Korea)

Abstract

In this paper, we study the continuity problem by an order of derivative for conformable parabolic equations. The problem is examined in both the linear and nonlinear cases. For the input data in suitable Hilbert scale spaces, we consider the continuity problem for the linear problem. In the nonlinear case, we prove the existence of mild solutions for a class of conformable parabolic equations once the source function is a global Lipschitz type in the Ls space sense. The main results are based on semigroup theory combined with the Banach fixed point theorem and Sobolev embeddings. We also inspect the continuity problem for the nonlinear model, and prove the convergence of the mild solution to the nonlinear problem as α tends to 1−.

Suggested Citation

  • Nguyen Huy Tuan & Van Tien Nguyen & Donal O’Regan & Nguyen Huu Can & Van Thinh Nguyen, 2023. "New Results On Continuity By Order Of Derivative For Conformable Parabolic Equations," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(04), pages 1-21.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:04:n:s0218348x23400145
    DOI: 10.1142/S0218348X23400145
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