Shahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-808811220210622Determination of unknown source term and boundary flux in a time-fractional inverse diffusion problemDetermination of unknown source term and boundary flux in a time-fractional inverse diffusion problem2712871677410.22055/jamm.2021.35292.1862FASedighehToubaei1 Department of Mathematics, Khuzestan Science and Research Branch, Islamic Azad University, Ahvaz, Iran,
2 Department of Mathematics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran.M.GarshsbiSchool of Mathematics, Iran University of Science and Technology, Tehran, IranParastooReihani ArdabiliDepartment of Mathematics, Payame Noor University, Tehran, IranJournal Article20201005In this work, we consider an inverse fractional parabolic problem that has many applications in different fields. Simultaneously determination of a source term and a boundary flux function in a time-fractional order parabolic equation is investigated using a mollified space marching method. Superposition and Duhamel's principles, the uniqueness of solution with respect to an over determination condition is proved. The stability and convergence of the numerical method are proved and two numerical test problems are conducted to illustrate the ability and accuracy of the numerical method. <br /> In this work, we consider an inverse fractional parabolic problem that has many applications in different fields. Simultaneously determination of a source term and a boundary flux function in a time-fractional order parabolic equation is investigated using a mollified space marching method. Superposition and Duhamel's principles, the uniqueness of solution with respect to an over determination condition is proved. The stability and convergence of the numerical method are proved and two numerical test problems are conducted to illustrate the ability and accuracy of the numerical method. <br /> https://jamm.scu.ac.ir/article_16774_8868049e5efe08584902ac865bd845d7.pdf