Hosseini, KamyarIlie, MousaMirzazadeh, MohammadBaleanu, Dumitru2022-03-112022-03-112021Hosseini, Kamyar...et al. (2021). "An analytic study on the approximate solution of a nonlinear time-fractional Cauchy reaction-diffusion equation with the Mittag-Leffler law", Mathematical Methods in the Applied Sciences, Vol. 44, no. 8, pp. 6247-6258.0170-4214http://hdl.handle.net/20.500.12416/5113The main aim of the current article is considering a nonlinear time-fractional Cauchy reaction-diffusion equation with the Mittag-Leffler law and deriving its approximate analytical solution in a systematic way. More precisely, after reformulating the nonlinear time-fractional Cauchy reaction-diffusion equation with the Mittag-Leffler law, its approximate analytical solution is derived formally through the use of the homotopy analysis transform method (HATM) which is based on the homotopy method and the Laplace transform. The existence and uniqueness of the solution of the nonlinear time-fractional Cauchy reaction-diffusion equation with the Mittag-Leffler law are also studied by adopting the fixed-point theorem. In the end, by considering some two- and three-dimensional graphs, the influence of the order of time-fractional operator on the displacement is examined in detail.eninfo:eu-repo/semantics/closedAccessApproximate Analytical SolutionExistence and Uniqueness of the SolutionFixed-Point Theorem,Homotopy Analysis Transform MethodMittag–Leffler LawNonlinear Time-Fractional Cauchyreaction–Diffusion EquationArticle4486247625810.1002/mma.7059