Tran Bao NgocBaleanu, DumitruO'Regan, DonalNguyen Huy Tuan02.02. Matematik02. Fen-Edebiyat Fakültesi01. Çankaya Üniversitesi2022-11-302025-09-182022-11-302025-09-182020Tuan, Nguyen Huy...et al. (2020). "On well-posedness of the sub-diffusion equation with conformable derivative model", Communications in Nonlinear Science and Numerical Simulation, Vol. 89.1007-57041878-7274https://doi.org/10.1016/j.cnsns.2020.105332https://hdl.handle.net/123456789/10850Tran Bao, Ngoc/0000-0003-1600-5845; Nguyen Huy, Tuan/0000-0002-6962-1898In this paper, we study an initial value problem for the time diffusion equation (C)partial derivative(beta)/partial derivative t(beta) u + Au = F, 0 < beta <= 1, on Omega x (0, T), where the time derivative is the conformable derivative. We study the existence and regularity of mild solutions in the following three cases with source term F: F = F (x, t), i.e., linear source term; F = F (u) is nonlinear, globally Lipchitz and uniformly bounded. The results in this case play important roles in numerical analysis. F = F (u) is nonlinear, locally Lipchitz and uniformly bounded. The analysis in this case can be widely applied to many problems such as - Time Ginzburg-Landau equations C partial derivative(beta)u/partial derivative t(beta)+ (-Delta)u = vertical bar u vertical bar(mu-1) u; - Time Burgers equations C partial derivative(beta)u/partial derivative t(beta)-( u center dot del) u + (- Delta)u = 0; etc. (C) 2020 Elsevier B.V. All rights reserved.eninfo:eu-repo/semantics/closedAccessConformable DerivativeNonlocally Differential OperatorDiffusion EquationExistence And RegularityGinzburg-Landau EquationBurger EquationArticle10.1016/j.cnsns.2020.1053322-s2.0-85085173305