NEW RESULTS FOR PARABOLIC EQUATION ON THE SPHERE WITH CAPUTO–FABRIZIO OPERATOR

Nguyen Anh Tuan, Nguyen Hoang Luc (), Nguyen Pham Quynh Trang and Ho Thi Kim van
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Nguyen Anh Tuan: Division of Applied Mathematics, Science and Technology Advanced Institute, Van Lang University, Ho Chi Minh City, Vietnam2Faculty of Technology, Van Lang University, Ho Chi Minh City, Vietnam
Nguyen Hoang Luc: Department of Mathematical Economics, Banking University of Ho Chi Minh City, Ho Chi Minh City, Vietnam
Nguyen Pham Quynh Trang: Department of Mathematics and Computer Science, University of Science, Ho Chi Minh City, Vietnam5Vietnam National University, Ho Chi Minh City, Vietnam6Faculty of Computer Science and Engineering, ThuyLoi University, No. 02, Truong Sa Street, Ward 17, Binh Thanh District, Ho Chi Minh City, Vietnam
Ho Thi Kim van: Division of Applied Mathematics, Thu Dau Mot University, Binh Duong Province, Vietnam

FRACTALS (fractals), 2022, vol. 30, issue 05, 1-13

Abstract: In this paper, we are interested in studying the initial value problem for parabolic problem associated with the Caputo–Fabrizio derivative. We deal the problem in two cases: linear inhomogeneous case and nonlinearity source term. For the linear case, we derive the convergence result of the mild solution when the fractional order α → 1− under some various assumptions on the initial datum. For the nonlinear problem, we show the existence and uniqueness of the mild solution using Banach fixed point theory. We also prove the convergence result of the mild solution when the fractional order α → 1−.

Keywords: Nonlocal Parabolic Equation; Banach Fixed Point Theory; Sphere; Regularity; Caputo–Fabrizio Operator; Convergence (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22401582

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