The Continuity by Order Derivative for Conformable Parabolic Equations with Exponential Nonlinearity

 In this article, we examine the continuity according to the derivative order of conformable parabolic equations. We establish the existence and uniqueness of mild solutions to the problem of source function exponential non-linearity. We prove the existence and uniqueness of a mild solution based on...

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Bibliographic Details
Published inElectronic Journal of Applied Mathematics Vol. 3; no. 1; pp. 42 - 63
Main Authors Ho Duy, Binh, Nguyen, Dinh Huy, Nguyen Van, Tien, Le, Dang Khoa
Format Journal Article
LanguageEnglish
Published 28.03.2025
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Summary: In this article, we examine the continuity according to the derivative order of conformable parabolic equations. We establish the existence and uniqueness of mild solutions to the problem of source function exponential non-linearity. We prove the existence and uniqueness of a mild solution based on some Sobolev embeddings, the Banach space of all continuous functions, and the Banach fixed point theorem. In addition, we will address the nonlinear model's continuity issue and demonstrate the mild solution's convergence to the nonlinear problem when \(\gamma'\to \gamma\).
ISSN:2980-2474
2980-2474
DOI:10.61383/ejam.202531101