Nguyen, Van TienBaleanu, DumitruNguyen, Van ThinhNguyen, Anh Tuan2024-01-172025-09-182024-01-172025-09-182023Nguyen, Anh Tuan;...et.al. (2023). "On the Fractional Diffusion Equation Associated With Exponential Source and Operator With Exponential Kernel", Journal Of Computational And Nonlinear Dynamics, Vol.18, No.5.1555-14231555-1415https://doi.org/10.1115/1.4062198https://hdl.handle.net/20.500.12416/15055Nguyen, Van Thinh/0000-0002-7408-2585; Nguyen, Van Tien/0000-0002-0975-9131In this paper, we investigate the well-posedness of mild solutions of the time-fractional diffusion equation with an exponential source function and the Caputo-Fabrizio derivative of a fractional order a is an element of ( 0 , 1 ). Some linear estimates of the solution kernels on Hilbert scale spaces are constructed using a spectrum of the Dirichlet Laplacian. Based on the Banach fixed point theorem, the global existence and uniqueness of the small-data mild solution are approved. This work is considered the first study on the time-fractional diffusion equation with a nonlinear function for all common dimensions of 1, 2, and 3.eninfo:eu-repo/semantics/closedAccessCaputo-FabrizioExponential NonlinearityGlobal Well-PosednessGlobal ExistenceArticle10.1115/1.40621982-s2.0-85194531859