Shahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-808810120200521Fractional-order Model for Cooling of a Semi-infinite Body by RadiationFractional-order Model for Cooling of a Semi-infinite Body by Radiation881051528110.22055/jamm.2020.28911.1697FAShahrokhEsmaeiliDepartment of Mathematics, University of Kurdistan, Sanandaj, Iran0000-0002-0584-6094Journal Article20190314In this paper, the fractional-order model for cooling of a semi-infinite body by radiation is considered.<br />In the supposed semi-infinite body, the equation of heat along with an initial condition and an asymptotic boundary condition form an equivalent equation in which the order of derivatives is halved.<br />This equation and a boundary condition introduced by the radiation heat transfer give rise to an initial value problem, whose differential equation is nonlinear and fractional order.<br />The semi-analytical solution to this nonlinear model was determined asymptotically at small and large times.<br />Moreover, two numerical methods including Grunwald-Letnikov approximation and Muntz-Legendre approximation yield numerical solutions to the problem.In this paper, the fractional-order model for cooling of a semi-infinite body by radiation is considered.<br />In the supposed semi-infinite body, the equation of heat along with an initial condition and an asymptotic boundary condition form an equivalent equation in which the order of derivatives is halved.<br />This equation and a boundary condition introduced by the radiation heat transfer give rise to an initial value problem, whose differential equation is nonlinear and fractional order.<br />The semi-analytical solution to this nonlinear model was determined asymptotically at small and large times.<br />Moreover, two numerical methods including Grunwald-Letnikov approximation and Muntz-Legendre approximation yield numerical solutions to the problem.https://jamm.scu.ac.ir/article_15281_94feec9fe604faf086e626c8718565f2.pdf