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Shavkat AlimovDepartment of Mathematics, National University of Uzbekistan, Tashkent, UzbekistanRavshan AshurovLaboratory of Differential Equations and their Applications, Institute of Mathematics of the Academy of Sciences, Tashkent, UzbekistanR GorenfloY LuchkoM YamamotoA KubicaOA PskhuM RuzhanskyN TokmagambetovB TorebekR AshurovLaboratory of Differential Equations and their Applications, Institute of Mathematics of the Academy of Sciences, Tashkent, UzbekistanO MuhiddinovaJ ChengJ NakagawaT YamazakiS TatarS UlusoyZ LiY HatanoS WangM D'ovidioP LoretiA MomenzadehS AhrabiJ JannoY FayzievR ZunnunovS AlimovDepartment of Mathematics, National University of Uzbekistan, Tashkent, Uzbekistan
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Аннотация
It is considered the inverse problem of identification the order of the fractional Riemann -Liouville derivative in time in the abstract subdiffusion equation, the elliptical part of which is a self-adjoint positive operator with a discrete spectrum. It is proved that the norm ||u(t)|| of the solution at a fixed t = t 0 restores uniquely the order . At the same time, an interesting effect was discovered: for sufficiently large t, the norm ||u(t)||, considered as a function of , is monotolically decreasing. A number of examples of concrete subdiffusion equations are discussed.
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