A 2D Convolution Kernel Determination Problem for the Time-Fractional Diffusion Equation
Durdiev D.K. Akylbayev M. Maxumova Z. Iskakova A.
March 2024Pleiades Publishing
Lobachevskii Journal of Mathematics
2024#45Issue 31044 - 1058 pp.
Abstract: In this article, two dimensional inverse problem of determining convolution kernel in the fractional diffusion equation with the time-fractional Caputo derivative is studied. To represent the solution of the direct problem, the fundamental solution of the time-fractional diffusion equation with Riemann–Liouville derivative is constructed. Using the formulas of asymptotic expansions for the fundamental solution and its derivatives, an estimate for the solution of the direct problem is obtained in terms of the norm of the unknown kernel function, which was used for studying the inverse problem. The inverse problem is reduced to the equivalent integral equation of the Volterra type. The local existence and global uniqueness results are proven by the aid of fixed point argument in suitable functional classes. Also the stability estimate is obtained.
Caputo fractional derivative , Cauchy problem , Fox’s function , integral equation , Mittag-Leffler function
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Bukhara Branch of the Romanovskii Institute of Mathematics of the Academy of Sciences of the Republic of Uzbekistan, Bukhara, 200117, Uzbekistan
Peoples’ Friendship University named after Academician A. Kuatbekov, Shymkent, 160012, Kazakhstan
Bukhara Branch of the Romanovskii Institute of Mathematics of the Academy of Sciences of the Republic of Uzbekistan
Peoples’ Friendship University named after Academician A. Kuatbekov
10 лет помогаем публиковать статьи Международный издатель
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